As Fender62 says, there's a strong possibility that the graphics chip on the motherboard is dead. Because the motherboard is designed as a single, integrated component, you can't just replace the graphics chip. You either need to replace the motherboard as a whole or try a separate graphics card.
However I'd be wary of buying a graphics card in case the entire motherboard is dead. Much as I hate recommending that people pay a computer technician for their services, this might be a case where it's necessary. That's because any decent repair shop should have a spare graphics board to hand, so that they can see whether installing it fixes the problem.
Alternatively (given the horrendous rates that some repair shops charge), if it's an old PC anyway and you only use it for web browsing, word processing, etc, (rather than for high-end gaming or video editing) it might be best to replace it altogether. (I can tell you where to buy a guaranteed Windows 7 PC from a firm I trust for around £90 including carriage. I can also tell you how to get all of your files off your old hard drive for only a few quid. That might be better than spending lots of money on fixing your old PC).