Open the computer & visually inspect the motherboard.
What you are looking for is bad capacitors.
The capacitors look like little tin cans sticking up on the motherboard.
If any have a domed or bulging top they are bad
If any appear to be oozing or leaking something they are bad.
Go here for more info.http://badcaps.net/pages.php?vid=5
If you click on the pictures to the right they get bigger.
Here is a good example of bad capacitors,http://badcaps.net/images/caps/kt7/kt3.html
Notice the tops are domed.
They should be flat.
If your motherboard has bad caps the simplrst way to fix it is to replace the motherboard.
If it passes the visual inspection try replacing the CMOS battery on the motherboard.
Be careful not to break the little plastic battery retainers on the battery socket.
Opposite the 2 retainers there is a small metal retainer .
If you take something like a small flatblade screw diver & compress the retainer toward the outside of the socket the battery should pop up slightly & you can remove it from the socket.
If that doesn't fix it I suggest trying a different power supply.
It will probably be suggested that you can test the power supply by jumping 2 of the wires on the main connector with a paper clip & use a multimeter.
Ignore that suggestion.
All you will learn is ,
A. it comes on
B. What the readings are at a "idle" .
A power supply is at it's heaviest load during startup.
The only way to test it properly is under a load with a actual power supply tester.
A power supply can appear to work properly at a idle but fail to put out enough power on all leads under a load.
If none of that fixes it I suggest the motherboard is failing.
A motherboard can fail with no visible signs .
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