Custom-built? It may be an issue of insufficient power supply. In this case, get a more powerful PSU for your system.
I don't understand what slot are you referring to. What I meant was the power supply from the PSU is insufficient to support the entire system including the graphics card. One way to confirm this is to replace it with a spare, weaker graphics card (or use the on-board graphics card if there is one) and check whether the same issue occurs.
If nothing works, it could be a sign of failing graphics card. If you are still using AGP card, get a PCI graphics card and see if it works.
If you are using a PCI card, slot into other PCI slots and see it works. Or get a second hand AGP card to try out.