Suggest you see if the problem is the Power On switch, or the Power Supply.
(First check to see if the receptacle in the surge protector, that the computer is plugged into, has power.
Have had a few bad surge protectors, where just THAT receptacle was bad.
"Hmmm, surge protector power on LED light is lit. Monitor, printer, and router have power, that are plugged into the surge protector.
Plugged a lamp into THAT receptacle, and found it to be bad)
To test whether the Power On switch, or the Power Supply is bad, a jumper wire is used to bypass the Power On switch.
[ The Power On switch is located inside the plastic Power On button.
This is an example of a generic ATX Power On switch, that I have found fits many computers,http://www.directron.com/atxswitch.html
The jumper wire is used on the 20, or 24-pin ATX main power cable's connector.
While still plugged into the motherboard.
The jumper wire connects to the Soft Power On wire, (Green), and to any Ground wire. (Black)
Example of a 20-pin ATX main power cable, and it's respective connector,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
Example of a 24-pin ATX main power cable, and it's respective connector,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain24
Using the jumper (Wire) to bypass the Power On switch, turns the Power Supply on?
The problem is a bad Power On switch.
Using the jumper to bypass the Power On switch, does Not turn the Power Supply on?
The problem is a bad Power Supply.
There is a correct procedure for performing this test.
Post back in a Comment if you wish to know.