If it doesn't POST, it's a hardware error. I would do the following:
- Remove everthing from the mainboard, except CPU and PSU. If it gives a beep, proceed with step 5
- try another PSU.
- try another CPU.
- try another mainboard.
- Connect components until you find the one which causes the trouble. Blow in every connector to clean it from dust. Start with the memory.
- Keyboard
- Graphic card
- Harddrive
- the rest, one by one
- If you've put back everything and it works again, it was maybe a loose connection.
- Make a backup and keep it up to date. Will save your life.
Hope that helps