Does your computer even make a beep when you first turn it on? If not then it could be a hardware problem and something like the RAM needs to be reseated. If that doesn't work then it could be your CPU, motherboard or PSU...
Whatever you have a spare of try switching it out. So before you go and try reseating your CPU or something then try a different power supply if you have one if you have already tried reseating the RAM.
You have to turn off onboard graphics in the BIOS if you put another card in so leave the other card out because it doesn't seem like the graphics is the problem quite yet.
1. Reseat the RAM
2. Try another power supply if you have one
if still nothing then make sure only the RAM is plugged into the board and disconnect the Hard drives, cd-roms, floppy, whatever is connected take it out.
You basically want nothing besides power to the board and of course leaving the restart button, power button and PC Speaker connected so you can power on, and listen to beeps if they arise.
If reseating RAM and switching out the power supplies doesn't fix it then it could be the CPU or mobo that's failed.