Okay. You could always buy a new computer. 8 years is a long time in the pc tech world.
But il be nice and help
You need to troubleshoot to find the problem. (starting with the PSU -> Motherboard -> CPU)
I can only troubleshoot the psu and the ram the rest i dont know yet.
But its likely to be the Power Supply Unit (PSU) that is faulty. (it can also be the RAM too but thats why you need to check the PSU first. And in worst case, the CPU can be faulty/dead)
Running fans and/or the motherboards LED's turn on dosnt necessarily indicate that the psu is okay. It might be faulty so the best way to do this is if you borrow a psu from someone or buy a new one but please try to borrow one first. It needs to be around 500-600 watt
1. Start with the old PSU: (easy part)
To check it follow the instructions on:
http://www.silverstonetek.com/downloads/QA/PSU/PSU-Paper%20Clip-EN.pdf
Remember to unplug the power cords on every component and remember where they should be.
If its faulty then the fan (on the psu) might not work or the fan will turn on and of multiple times as long there is power. (if it start to smoke then cut the power!)
If its faulty then that's good. You only need to buy a new psu.
If the fan (on the psu) works then it isnt faulty but then some other component is. You'll need the borrowed/new psu to test the rest of the computer.
(Its always a good idea to try with a another psu just to be sure if its actualy the psu that causes the problem)
(A bit more of a challenge)
2. If it is faulty / not working like it should, then install the one you borrowed or bought (please try to borrow one). If it boots up like normal then congrats.
If it didnt boot up normally but still have the same problem then its the RAM or CPU.
If it boots up but you hear Long Single Beeps or series of short beeps then there is a problem with the RAM.
If it boots up but you hear one long beep and several short beeps then that indicate that you're missing a graphic card (but thats highly unlikely You'll hear if the motherboard have a integrated graphic card i think)
- Take out all the Memory sticks (RAM) except for one (The hard part now is to find the right slot to connect it unless you have the motherboard manual. If you connect it to the wrong slot it might just turn on and off or beep) The power need to be off when changing it!
- If it dosn't work whit any of the ram sticks then buy new onesw. If it still dosn't work then it might something on the motherboard or the CPU.
There may be some errors with what i've written as im writing this in a hurry. Check out this links.
Advance troubleshoot if you have build the computer self but there is some helpful tips.
http://www.tomshardware.co.uk/forum/261145-31-perform-steps-posting-post-boot-video-problems
Go down to the Best Solution part. It explain some of the stuff i wrote.
http://www.tomshardware.co.uk/forum/302360-31-computer-turns-split-shuts
If you need more help than just ask