It sounds like the issue is with your video card (integrated part of your motherboard) overheating GPU IC or solder connections around the GPU that becomes lose during usage due to heat. A reflow might help. Hope this helps, good luck.
This is true that's the problem of the Dell D630 and others Dell with 128MB Nvidia Graphics card that over the years the heat sink fails for lack of cleanliness or cream to dissipate heat loses strength. I fixed many Dell D630 with this problem reflowing the Video card. To do this you need to completely disassemble the computer and remove the motherboard. Once motherboard is out clean all heat sink cream with alcohol and remove all extras (paper and plastics stickers / whites and blacks, ram, modem, cables, button board, etc.) leaving it bare bone. Preheat conventional oven to 375F degrees (No Microwave) and bake (Yes you read right bake it) the motherboard for 8 min. (Look out! it hot) Cool rapidly using a fan. Rearm all over again but this time use a good heat sink cream and make sure the heat sink copper parts is firmly attached to the video card (Don't use the old grey foam that brings the video card from factory) put the cream directly on the video chips. This work 200% fine good luck!... If the problem persists you can do the process again the secret is keeping the video card coldest possible.