The T-2792 is one of the 14 eMachines models with a high failure rate. In most cases like what you describe, the motherboard has gone dead, sometimes ruining the power supply in the process. (Not the other way around, as in most machines, when the power supply ruins the motherboard.) You can replace the Motherboard for $159.95 plus shipping from eMachines tech support.
The hard drive, modem, and memory remain good, but without good luck, you will not make a easy fix. If you do not use an eMachines motherboard replacement, the hard drive will not work, and you will not be able to use the three recovery disc set.
You should, however, test the machine with a borrowed power supply, as sometimes the power supply just fails for no good reason and the motherboard remains OK.
With some clever hoops jumping, you can use the drive in another configuration and get the Windows XP ID registered with Microsoft over the phone... but the recover discs will still not work as they require the EEPROM code or tattoo of the eMachines motherboard as a condition of the Microsoft license.
You can buy another motherboard as cheaply as $49, that will be reliable... and buy Windows OEM for $64 if you do not have success with Microsoft registering this version that is on the hard drive... Still a much better option than fixing the computer with eMachines junk. Look for "Motherboard Combos" at various online sites such as
www.directron.com,
www.tigerdirect.com,
www.newegg.com,
www.zipzoomfly.com,
www.outpost.com,
www.techdepot.com,
www.cdw.com,
www.pcconnections.com,
www.krex.com, and many others. They come with a motherboard and a CPU. You just have to be sure your new board will use the DDR PC2700 or DDR PC3200 memory that is already installed.