NO audio output. Unit is on, illuminated, and so on, but no audio output to any of the speakers

What system does it have ? Base or up level ,does it have a amp ? Do you know what a RPO code is ? Without testing no one could say for sure what the issue is . First off would need to know what system we are dealing with .
RPO Options
The entertainment system on this vehicle is configured with either a base or uplevel audio system. Both the base and uplevel audio systems contain a radio, antenna, and speakers.
The following shows the Enteratinment RPOs that are available for this vehicle:
• (UM7) AM/FM Stereo
• (U1C) AM/FM Stereo CD
• (US8) AM/FM Stereo, CD, MP3, RDS, EQ
• (US9) AM/FM Stereo, 6-Disc CD, MP3, RDS, EQ
• (UXQ4) Base Four Speaker
• (U79) Uplevel Four Speaker
• (WBM) Premium Audio
• (U2K) Digital Radio

Circuit Operation
Radio Power: The main radio power is supplied by the 10A RADIO (BATT1) fuse in the body control module (BCM). Radio switch-on power, 12 volts in ACC, RUN or RAP, is supplied by the 10A RADIO (ACC.) in the BCM.
Radio Grounds: The main radio ground provides a ground for the radio circuits. An additional braided ground strap provides a shielding radio case ground to reduce EMI noise. Both grounds are connected together inside the radio.
Radio Speaker Outputs: At zero volume, the plus (+) and minus (-) speaker outputs are both approximately 5-6 volts, measured to vehicle ground. If a plus or minus for any speaker output is shorted to ground or voltage, the radio circuitry will turn OFF all 4 speaker outputs for component protection. Above zero volume, the plus and minus change to create a voltage difference between each other, to drive the voice coil of the speaker.
Radio Park Lamp Input: The radio park lamp input allows the radio to sense when the vehicle parking lamps are ON. When the parking lamps are ON, this circuit goes to battery voltage, and the radio display back-lighting switches from full bright to the brightness level determined by the I/P illumination input.
Radio I/P Illumination Input: A pulse width modulated (PWM) voltage for instrument panel (I/P) illumination is provided to the radio I/P illumination input. The Radio uses this input to directly illuminate the radio buttons and adjust the radio display back-lighting when the park lamp input is ON.
Amplifier Power: The main amplifier power is provided by the 20A PREM AUDIO fuse in the instrument panel fuse block..
Amplifier Radio Speaker Inputs (WBM only): The radio speaker outputs, at a reduced output level for amplified systems, are the amplifier inputs. The amplifier boosts these inputs and outputs them to the vehicle speakers. Speaker plus and minus circuits from the radio change to create a voltage difference between each other. If one speaker plus or minus is open between the radio and the amplifier, the input to the amplifier is approximately half because only one of the circuits is changing. The speaker for that channel then operates at approximately only half the normal volume.
Amplifier Speaker Outputs (WBM only): At zero volume, the plus (+) and minus (-) speaker outputs are both approximately 5-6 volts, measured to vehicle ground. If a plus or minus for any speaker output is shorted to ground or voltage, the amplifier circuitry will turn OFF either the front outputs or rear outputs for component protection. Above zero volume, the plus and minus change to create a voltage difference between each other, to drive the voice coil of the speaker.
Amplifier Radio-On (WBM only): When the radio is ON, this circuit is pulled to 12 volts by the radio. The amplifier switches ON when this circuit is 12 volts and switches OFF when this signal is 0 volts.
Remote Radio Audio Signal Inputs (UE1 only): Audio output from the OnStar® communications module connects to the remote audio signal inputs of the radio. When the cellular telephone mute signal goes to 0 volts, the radio over-rides any other audio signal and uses these inputs as the source for output to the speakers.
Cellular Telephone Mute (UE1 only): The OnStar® communications module uses the cellular telephone mute signal circuit to over-ride the radio for OnStar® communication. When cellular telephone mute is not active, this circuit is held at 2 volts by the radio. When the cellular telephone mute signal is pulled to ground, the radio over-rides any other audio signal and uses the remote audio signals as the source for output to the speakers. If the radio was OFF when this circuit is pulled low, the radio will turn ON. Additionally, the radio fades the speakers to full front, adjusts the volume to an initial audible level, and sets an AutoTone designed for optimal use with OnStar®. When the mute signal is no longer pulled to ground, the radio returns to the mode it was in previously.

Hooking up a professional or factory scan tool that can read radio codes would be one of the first test's to do .
DTC B1025, B1035, B1045, or B1055 (w/out RPO WBM)
DTC B1025, B1035, B1045, or B1055 (w/ RPO WBM)
DTC B1030, B1040, B1050, or B1060 (w/ out RPO WBM)
DTC B1030, B1040, B1050, or B1060 (w/ RPO WBM)
DTC B1259
The following conditions are present for 250 ms or longer:
B1025 - B1055 01
One of the speaker positive output circuits is shorted to battery.
B1025 - B1055 02
The speaker positive output circuit is shorted to ground.
B1025 - B1055 04
The speaker positive output circuit is open.

Your best bet , take it to a qualified repair shop .

If you use a wire harness adapter, you just have to match the colors from the Kenwood plug to the wires in the adapter. No guesswork.

Kenwood uses the CEA standard for car audio wiring:

Yellow: 12VDC constant power
Red: 12VDC key-switched power
Black: Ground
Orange/White: Illumination
Blue/White: Remote output for amp turn-on
Blue: Power antenna activation

White: Left front speaker (+)
Gray: Right front speaker (+)
Green: Left rear speaker (+)
Violet: Right rear speaker (+)

Each wire with a black stripe is a negative speaker output.

You can download owners' manuals from Kenwood's web site.

http://manual.kenwood.com/en_contents/search

its blown or unhooked

Either that speaker is not connected or, the speaker is blown. To test: Disconnect that speaker from the stereo and, using a 9volt battery, tap the speaker's + and - to the battery's + and -. You should hear a "pop". That would indicate that the speaker works. DO NOT connect the 9 volt battery to the stereo side of the speaker wire!!!!

2007 Toyota Sienna Car Audio Wiring Color Codes
Car Radio Battery Constant 12v+ Wire: Blue/Yellow
Car Radio Accessory Switched 12v+ Wire: Gray
Car Radio Ground Wire: Brown
Car Radio Illumination Wire: Green
Car Stereo Dimmer Wire: N/A
Car Stereo Antenna Trigger Wire: Black/Red
Car Stereo Amp Trigger Wire: N/A
Car Stereo Amplifier Location: N/A
Car Audio Front Speakers Size: N/A
Car Audio Front Speakers Location: N/A
Left Front Speaker Positive Wire (+): Pink
Left Front Speaker Negative Wire (-): Violet
Right Front Speaker Positive Wire (+): Green
Right Front Speaker Negative Wire (-): Blue
Car Audio Rear Speakers Size: N/A
Car Audio Rear Speakers Location: N/A
Left Rear Speaker Positive Wire (+): Black
Left Rear Speaker Negative Wire (-): Yellow
Right Rear Speaker Positive Wire (+): Red
Right Rear Speaker Negative Wire (-): White

yes, there is an amp turn-on wire from the head unit (black with a red stripe). You will need to add a power wire and fuse from the fuse box to run the amp. You can use the speaker outputs as inputs to the amp, depending on what you are trying to do. Please let me know if you need more help, and identify the amp model as well as the speakers you will connect.

Car Radio Battery Constant 12v+ Wire: Blue/Yellow
Car Radio Accessory Switched 12v+ Wire: Gray
Car Radio Ground Wire: Brown
Car Radio Illumination Wire: Black/Red
Car Stereo Dimmer Wire: N/A
Car Stereo Antenna Trigger Wire: N/A
Car Stereo Amp Trigger Wire: Black/Red
Car Stereo Amplifier Location: Under the center console.
Car Audio Front Speakers Size: N/A
Car Audio Front Speakers Location: N/A
Left Front Speaker Positive Wire (+): Pink
Left Front Speaker Negative Wire (-): Violet
Right Front Speaker Positive Wire (+): Green
Right Front Speaker Negative Wire (-): Blue
Car Audio Rear Speakers Size: N/A
Car Audio Rear Speakers Location: N/A
Left Rear Speaker Positive Wire (+): Black
Left Rear Speaker Negative Wire (-): Yellow
Right Rear Speaker Positive Wire (+): Red
Right Rear Speaker Negative Wire (-): Yellow

If you only have powered speakers for both mains and monitors, you will NOT use the Speakon outputs on the back.

You will connect USING BALANCED TRS audio cables from the MAIN L and R jacks on the top of the unit to your powered main speakers and also connect the monitor speakers by TRS balanced connections to the MON1 and MON2 1/4 inch jacks on the top deck of the unit.

POWER ALL the speakers AND the mixer from the same receptacle or power source/conditioner.
This may mean running an extension cord alongside your audio snake from the stage. Failure to do do this can cause damage due to exceeding the common mode noise (ground bounce) of different power sources.

Leave the speaker slide switch in the Main L/R.

Adjust the rotary knobs for Mon1 and MON2 for each channel to proportion each to the monitor "mixes" which you will control overall with the MON1 and MON2 sliders.
You will use the MAIN slider to control the mains level.

To set the trims for each channel, push the PFL so only that LED illuminate red... then at max inout level for the channel, use the LED bar graph on the right side so it is just a little below the clip level where the top LED's of the bar graph do not illuminate.

1992 Pontiac Grand Am Car Radio Stereo Audio Wiring Diagram
Car Radio Battery Constant 12v+ Wire: Orange
Car Radio Accessory Switched 12v+ Wire: Yellow
Car Radio Ground Wire: Black
Car Radio Illumination Wire: Gray
Car Stereo Dimmer Wire: Brown
Car Stereo Antenna Trigger: Pink
Car Stereo Amp Trigger Wire: N/A
Car Stereo Amplifier Location: N/A
Car Audio Front Speakers Size: N/A
Car Audio Front Speakers Location: N/A
Left Front Speaker Positive Wire (+): Tan
Left Front Speaker Negative Wire (-): Gray
Right Front Speaker Positive Wire (+): Light Green
Right Front Speaker Negative Wire (-): Dark Green
Car Audio Rear Speakers Size: N/A
Car Audio Rear Speakers Location: N/A
Left Rear Speaker Positive Wire (+): Brown
Left Rear Speaker Negative Wire (-): Yellow
Right Rear Speaker Positive Wire (+): Dark Blue
Right Rear Speaker Negative Wire (-): Light Blue

Good luck and merry xmass

Use the speaker wire outputs on the wiring harness on the back of the radio. The RCA outputs are for using an external amplifier, so you do not want to use them. The speaker wires should be color coded. The front speakers are normally grey and grey with a black stripe for one side, and then white and white with a black stripe for the other side (left and right sides)

The rear speakers are violet and violet with a black stripe and the other rear is green and green with a black stripe. All the solid colors are the positive speaker output and the wires with the black stripe are the negative speaker outputs.

These speaker outputs are on the same harness as the power connections to power up the radio. I believe that it has more than 10 wires on it. I am not sure what socket you speak of that is 10 pin and has speaker outputs. The speaker outputs alone are 8 wires, so the harness will have more than 10 wires. It also has the yellow wire for constant 12 volts to keep memory, the red wire to connect to 12 volts when the vehicle is on, and the black wire for the ground. Then it should also have a blue wire for use with an external amplifier to turn it on or to use for a power antenna to turn it on. You may also find several other wires on it like the orange for illumination and brown for muting the radio when a phone is in use. Those last few wires do not need to be used unless you want them for a specific purpose.

you can find all kinds of adapters for RCA or phone jack to anytype of connectors at best buy or circuit city, if not Radioshak probably have them. just ask for a cable adapter to the type of connector transformation you need for the speakers.