Emachine Wiring Diagram

What a Marvelous person!

You have described a 4-pin Peripheral power cable, ('P6'),

http://www.playtool.com/pages/psuconnectors/connectors.html#peripheral

An IDE harddrive, of which the 4-pin Peripheral power cable example, is plugged into.
Another look at an IDE (PATA) harddrive,

http://www.newegg.com/Product/Product.aspx?Item=N82E16822136096

http://en.wikipedia.org/wiki/Parallel_ATA

However, I do not know if the flat IDE ribbon cable marked Slave, goes to a secondary Harddrive, or an optical drive. (CD/DVD drive)

Either way the point is moot. BOTH of those 'squarish flat black' units, HAVE a 4-pin Peripheral power cable to them.
Another hardware component, those type of power wires CAN go to, is a computer case fan.

However not ALL power cables have to be used. Sometimes there are extra ones. These are in case they are need later.

To summarize;
The optical drive, or drives; that you put a CD, or DVD disk in; can use a 4-pin Peripheral power cable.
(IDE/PATA optical drive)

Harddrive's can use a 4-pin Peripheral power cable.
(IDE/PATA harddrive)

A computer case fan may use a 4-pin Peripheral power cable.

Or the 4-pin Peripheral power cable you see, may simply be an extra one. One if needed in the future.

The eMachines T2245 uses a Trigem (Manufacturer), Imperial GLVE (Model name), motherboard,

http://www.ebay.com/itm/New-Emachines-Imperial-GL-VE-20021218-Motherboard-Socket-478-System-Board-/121098707716?pt=Motherboards&hash=item1c320ba304

Supports an IDE (PATA) harddrive, (Or 2 of them)
Supports an IDE (PATA) optical drive, (or two of them)

I DO hope you are following Anti-Static Procedures!

Your body carries Static electricity. Static WILL fry out (Short Circuit), the delicate hardware components inside a computer.
Relieve your body of Static, BEFORE reaching inside your computer.

Computer on a table, computer Unplugged from power, computer case open;
TOUCH an unpainted surface, of the metal frame of the open, empty computer case.
This action will relieve your body of Static.

IF, you leave your computer in the middle of working on it, be SURE to Touch the metal frame again upon your return.

Also I would like to add;

http://computer.howstuffworks.com/

http://www.hardwaresecrets.com/article/Anatomy-of-a-Hard-Disk-Drive/177

http://www.hardwaresecrets.com/article/Anatomy-of-an-Optical-Drive/179

For additional questions please post in a Comment.
Regards,
joecoolvette