Well, since you're just 'Killin Time', replace the power supply.
Your power supply has a weak voltage rail. (Your power supply has a 3.3 volt rail, a 5 volt rail, and a 12 volt rail) This is caused by a bad Electrolytic Capacitor or capacitors.
Electrolytic capacitors in a power supply are filters. They filter the final stage of the rectified DC electricity.
There are two main causes of capacitor failure, and the first cause CAN lead to the second one.
1.Most computer owners do not clean their power supply, and the inside of their computer out regularly. This causes the power supply to try to put out more power, because Heat = Wasted Energy
The power supply can only go so long in this condition, then components inside start to fail. The Electrolytic Capacitors are the weakest link.
Electrolytic capacitors are little aluminum 'cans'. They have a strip of metal with an insulating medium on it, another strip of metal, and a strip of paper soaked with Electrolytic Paste. These strips are stacked on each other, with the paper strip in the middle. Then they're rolled up tightly, and put in that 'can'. Two leads come off of the metal strips. One lead per strip.
Once the Electrolytic capacitor starts to fail, a gas is developed inside, and pushes against the seal for the 'can'. Electrolytic paste starts to ooze out, and when a cerain level of paste is oozed out, the capacitance of the electrolytic capacitor drops. Eventually when enough paste has oozed out, the capacitor fails.
2.There were a large supply of bad capacitors made. An electrolytic paste formula, was stolen from a large capacitor maker in the East.
Unknown to the thief, the thief was given access to a bogus formula.
The formula was know to develop gas inside, as an ingredient was found later to counteract this, but was not in this formula at this time.
MANY capacitors were made from this formula! They have been used a LONG time ago, and are still accidentally being used. All kinds of electronics use these capacitors. In the computer industry alone, many motherboard, and power supply makers went bankrupt, or almost bankrupt.
Good electrolytic capacitors come from Japan.
It is common knowledge that eMachines are cheaply made. This is why they're so cheap to buy. I have an old eMachines T1090 made in 2001 that I use for a loaner computer. Still going strong, but I changed the power supply. I believe eMachines is coming back. They are so cheap now so they can generate revenue to keep going.
What you hear are fans spinning, and your hardrive spinning in an endless loop. This is because the processor doesn't have enough power to come on. The processor in YOUR eMachines, is the hardware component that uses the most power. If you had a graphics card that took more power, then it would be the most power hungry component. But the processor comes on before a graphics card, so the point is moot.
Case fan/s spin, power supply fan spins, lights light up, processor fan spins, but after BIOS has run the memory count, it try's to start the processor, and there isn't enough power.
No processor, no Operating System. (Windows XP is an example of an O/S). No Operating System running, the harddrive spins in an endless loop, and the computer of course, doesn't work.
Have a power supply in another desktop, you can use for a test?
1.http://en.wikipedia.org/wiki/Electrolytic_capacitor
2.http://en.wikipedia.org/wiki/Capacitor_Plague
3.http://en.wikipedia.org/wiki/Computer_power_supply
4.http://www.dashdist.com/1u2u/company/capacitor.html
EDIT:
It ISN'T motherboard failure!!!
The computer doesn't come on at all! If it did, then shut off, it would mean bad electrolytic capacitors on the motherboard. SPECIFICALLY the capacitors surrounding the processor.
These are voltage regulators for the processor. The Processor has to have a Steady, Clean, supply of DC electricity. It has a TIGHT tolerance zone! This tolerance CANNOT vary by very much.
IT IS THE POWER SUPPLY. Plain an Simple!
EDIT 2:
Since WHEN does a Southbridge chip, control the Soft-Power On function of a power supply?
http://en.wikipedia.org/wiki/File:Motherboard_diagram.png
"There are two basic differences between AT and ATX power supplies: The connectors that provide power to the motherboard, and the soft switch. On older AT power supplies, the Power-on switch wire from the front of the computer is connected directly to the power supply.
On newer ATX power supplies, the power switch on the front of the computer goes to the motherboard over a connector labeled something like; PS ON, Power SW, SW Power, etc. This allows other hardware and/or software to turn the system on and off.
The motherboard controls the power supply through pin #14 of the 20 pin connector or #16 of the 24 pin connector on the motherboard. This pin (Usually the green wire but can be the grey wire Dependant on PSU manufacturer) carries 5V when the power supply is in standby. It can be grounded (connected to any black pins) to turn the power supply on without having to turn on the rest of the components. This is great for testing if you don't have a spare motherboard around, or don't want to connect a suspicious power supply to a working motherboard with risk of damaging it."