1) take your graphics card out then turn on your PC. If it comes on then its your graphics card. Try looking up some stuff that may cause that
2) If it still dont come on with the graphic card out then try a different Monitor.
3) If another monitor don't work. Get a professional Technician or try it yourself. Open the case and there is a jumper by a little battery called the CMOS Battery. Switch the jumper over to the other side of the pins, it should be 3 pins, and the jumper is over two of them, move it to the other two pins for about 10 minutes, Then try.
4) If that dont work it may be a problem with your PCI or AGP slot, go to the manufactor of the motherboard and look for other methods or get a new computer.