I need you to check something first.
I'm going to get detailed here to explain;
1) The Dell Dimension 1100 (B110) uses a 20-pin ATX main power cable,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
The above is a STANDARD pinout for the wires going into a 20-pin ATX main power cable's connector.
For a time period Dell had parts made for their computers, that were PROPRIETARY.
(All pre-built computer manufacturers have their computer parts made by somebody else)
They were Proprietary, in that the STANDARD guidelines for desktop computers was NOT followed.
They had the wires changed around for the 20-pin ATX main power cable.
They also had the pins in the 20-pin ATX main power connector, on the motherboard, changed also.
Means if you plug in an aftermarket Power Supply, it may toast the motherboard, Processor, Ram Memory, Harddrive, graphics card, (IF used), and so on.
Fun stuff huh?
Dell changed from being Proprietary as far as I know.
However you computer may fall into the old proprietary parts.
You need to compare the 20-pin ATX main power cable's connector, of the old Power Supply, TO the new Power Supply's 20-pin ATX main power cable connector.
SEE if those wires (Color code) are going into the same socket holes, as the old one.
Look at the Lock on the side, and use it for the key.
In the Standard 20-pin ATX main power cable's connector, Number 1 pin is the Orange wire, and on the side OPPOSITE of the Lock.
Number 11 wire is also Orange, but is on the same side as the Lock.
Now you have the key, check out the old Power Supply's 20-pin ATX main power cable's connector.
Same color of wires going into the proper socket holes in the main power cable's connector?
Whew! Good! Let's go on.
You need to get the Power Supply going.
Bypass the Power On switch.
IF, you bypass the Power On switch, and the Power Supply comes on, you have a bad $5 Power On switch.
IF you bypass the Power On switch, and the Power Supply does NOT come on, you have a bad Power Supply.
Test has NOTHING to do directly with the Power On switch, or it's wires.
A jumper wire is used on the Soft Power On pin, TO ANY Black wire, in the 20-pin ATX main power cable's connector,
Looking back at the 20-pin ATX main power cable,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
The GREEN wire is the Soft Power On wire.
A-N-Y Black wire you see is a Ground wire.
(The power wires are Positive wires. ALL Black wires are Negative wires )
The preferred jumper wire is a paper clip.
Straightened out, then bent into a U-shape.
The top of the U is wrapped a few times with black plastic electrical tape.
This taped area is for your fingers and thumb to hold onto.
Turn the U-shape upside down, and the 'Legs' are what you are going to use.
One leg goes down into a socket hole with the Green wire.
The other leg goes down into ANY socket hole that has a Black wire in it.
The 'Leg' of the jumper wire goes RIGHT NEXT TO the existing wire in the socket hole.
Where the wires go down into the connector of the 20-pin ATX main power cable, is the BACK.
The 20-pin ATX main power cable is plugged into the motherboard, as shown in the photo to the far right, in the Playtool link.
The jumper wire goes down into the Back of the connector, and into the two socket holes named above.
The jumper wire MUST go far enough down into the socket hole of the connector, to go PAST the insulation of the wire, AND touch the metal terminal at the end of the wire.
All wires going into the main power cable's connector, end in a metal terminal,http://www.molex.com/molex/products/datasheet.jsp?part=active/0002081202_CRIMP_TERMINALS.xml&channel=Products&Lang=en-US
The left side is the Back, and the part that get's crimped on the insulation of the wire. The right side is the Front.
The Front of those Molex metal terminals can be seen in the center photo, of the Playtool link.
Contact made is no more than 2 seconds.
(The Power On switch is A Momentary Contact Switch)
Get the Power Supply going, then post back in a Comment, as to the results.
(Also make SURE the 4-pin ATX +12 Volt power cable is plugged in,http://www.playtool.com/pages/psuconnectors/connectors.html#atx12v4
This is power for the Processor, and sometimes forgotten. NO, it has nothing to do with why the Power Supply does not come on. Just wanted to add.
This is where it plugs into the motherboard,http://support.dell.com/support/edocs/systems/dim1100/EN/SM/techov.htm#wp1061217
Processor and heatsink connector (J2E1) is where the Processor sits.
Processor power connector (J5B1) is where the 4-pin ATX +12 Volt power cable plugs in )
May I also ask why a new Power Supply was purchased, and a new motherboard?
Post back in a Comment.