|Stuff I would try, in order of importance:|
-First, make sure that the memory slots are free of dust.
-If there are more than two memory modules, try running each one by itself, and in both slots.
-Any bulging or leaking capacitors on the motherboard? If you can spot any, they're definitely causing problems. Hopefully you know someone who can solder.
-Run the machine without any add-on boards. Take out the video card, if you have one, and use the integrated video. Same with any modems, sound cards, etc. Disconnect all external peripherals except for the PS/2 keyboard. Run the system with the CPU, main hard drive, and ONE stick of RAM. If it works, install the extra components one at a time, till it starts acting up again.
-Try borrowing a spare power supply unit from a friend or local computer shop. Although this does not sound like a PSU problem, it's definitely worth a shot, as eMachines are known to have very cheap PSUs.
-Give it the finger and buy a new motherboard or system, as something's probably wrong with the core logic/chipset.
HTPC | Pentium M @ 2.82GHz | 4GB | 1.0TB | Radeon HD5750 | Blu-Ray | Win7 Pro | HDMI out to Onkyo TX-SR707