The beep you hear is a BIOS Beep Code. The computer's method of informing you something is wrong, and the area to look into for it.
The code is similar to what you may be used to.
(Afghanistan, Army? If so, hello brother/sister. 1st Cav, 13th Sig. Corp)
The BIOS Beep Code is similar to a Morse Code.
Two short beeps followed by a long beep, a pause of silence, then the pattern repeats, over, and over.
One short beep indicates everything is okay.
This is an indication that BIOS has concluded the Ram Memory count, and everything is 5 By.
According to my sources, the eMachines T2682 desktop computer uses an Imperial GV motherboard model, made by TriGem.
The front plastic cover of your computer is the Front Panel.
The area on the motherboard that the cables, (Wires), attach to on the motherboard, is the Front Panel header.
This is the Front panel header pinout, for the TriGem Imperial GV motherboard,http://www.e4allupgraders.info/dir1/ecase/support/front_panel_support.shtml
On this page I would like you to scroll down to the heading -
Imperial GV Front Panel Motherboard Pinouts
Looking at the pinout;
1) Pin 1 is Not used. NC = No Connection
2) Pins 2 and 3 are for the Power On LED light
[Light Emitting Diode]
Pin 2 is for the Ground wire. (GND) ( - )
Pin 3 is for the LED light power wire. ( + )
3) Pin 4 is not used. NC
4) Pins 5 and 6 are for the Harddrive Activity light. (LED)
HDD is HarDDrive
Pin 5 is for the LED power wire
Pin 6 is for the HarDDrive signal wire
(If after attaching the wires the HDD LED light is dim, reverse the wires)
5) Pins 7 and 8 are for the Power On switch.
Pin 7 is for the Ground wire.
Attaching the Peripheral cables;
1) You have an IDE harddrive. Uses a 40-pin IDE ribbon cable.
(39 actually. One pinhole is blocked off)
There is a Locating Tab on one side of the IDE ribbon cable's connector.
Left-click on the blue IDE connector in the photo to the upper right.
At the top middle of the connector you will see two ridges.
This is the Locating Lug.
Now left-click on the IDE connector on the motherboard, shown in the photo to the upper right.
(To the right of the blue IDE connector)
Looking at the blue IDE connector on the motherboard, you will note there is a cutout on one side of the connector.
This is a Locating Slot.
Lining the Locating Lug up to the Locating Slot, puts the pins of the IDE ribbon cable's connector, in the correct position for the pinholes in the motherboard's IDE connector.
IF, your ribbon cable's connector does Not have a Locating Lug;
Look at the outside edge of the ribbon cable. You should see a faint Red stripe.
The Red stripe is always next to Pin 1.
Next to the motherboard's IDE connector should be a printout.
It will state PRI 1, (Stands for Primary 1), or IDE 1.
This is for the Harddrive.
[ If you see PRI 2, or SEC, (Secondary), this is for the optical drive.
(CD/DVD drive). Using this information, you will know the other IDE connector on the motherboard is for the Harddrive ]
That printout is always next to where Pin 1 is.
Therefore on the motherboard, the side of the IDE ribbon cable that has a Red stripe, will go next to the printout.
If your harddrive does not have a Locating Slot on it's IDE connector, Pin 1 is always towards the 4-pin IDE power pins.
The above is a webpage from Playtool.com, discussing the various power cables used in a PC, and more specifically the standard 4-pin Peripheral power cable.
I linked it to show you a standard 4-pin Peripheral power cable, plugged into an IDE harddrive.
(A Peripheral power cable's connector, has been misnomered as a Molex connector, repeatedly through the years.
This was the name given to the first connector of this design.
It's kind of like referring to an adjustable open-end wrench, as a Crescent wrench )
Here in the photo of the rear view of an IDE harddrive, (Photo to the far left), you will see the 4 power pins.
To the left of the power pins are the Jumper pins.
To the left of the jumper pins, is the IDE interface for the 40-pin IDE ribbon cable.
The Red stripe of the IDE ribbon cable goes towards those 4 power pins.
To be continued in an additional comment.