Does that system even has a video card or just the onboard video from the CPU? What exactly happens when you turn on the system? Does it sound like it's starting? Drive spinning, lights coming on? No screen at all even when the BIOS screen should be on?
Could be any number of things, from RAM to power supply to motherboard, a bad hard drive can cause issues, even a bad drive cable. Unplug the hard drive/CD/DVD, unplug from wall, reset BIOS with the jumper or pull out the CMOS battery for 10 seconds, hold in the power button for abotu 30 seconds. Reseat the RAM, if you have more than one stick, use only one stick. Plug in the system and see if it turns on. If it does and you see the BIOS screen, shut it off, plug it all back in and see if it turns on.