A lot of eMachines computers manufactured between late 2002 - 2004, even into early '05 contained the flawed Bestec ATX-250-12E power supply. This particular model has a flaw in the +5VSB rail, where the voltage will spike up to 8v, even 10v+, eventually frying the power supply itself, as well as your motherboard's chipset. When this has occurred, even after you replace the power supply, the computer will do nothing more than spin the fans when you press the power button.
I have the Bestec ATX-250-12Z model which was built with an overload surge protector that thankfully saved the motherboard. The 5+VSB (5+ Volt Stand By) rail went bad because I have been using the sleep mode since my computer was new. Older eMachines & HP have been using these poorly made power supplies if you have a Bestec I'd change it right away.