Judging by the age of that thing it is very likely that its capacitors are gone bad by now.
Check this page:
Then inspect the mainboard visually to see if you have any bad capacitors.
If yes, then if you have the skill and tools you can try to replace them with some new ones. If not, there are repair shops doing it for a small fee.
If you don't notice anything extraordinary on the mainboard, disconnect all drives and try powering it on without video card and memory sticks -- if that gets you some beeping then the board and CPU are ok but the video card or RAM are defective. If not, then you should check for the bent or broken CPU pins.
Basically, it is a troubleshooting process -- unplug all devices and if it works, plug them back one by one until you find the one which is stopping it from working. I wouldn't get my hopes too high though. That thing is ancient history (some 11 years old or something). Good luck.