If you've gotten here, you most likely have an issue with your GPU due to this recall: Dell Blog Post about NVIDIA GPU Recall

To fix this, you can try to "re-flow" the soldier on the motherboard, which should give you a little more life out of the laptop.

Follow this guide to remove your motherboard: D820 Motherboard Removal

Once you have remove the motherboard, clean off all of the thermal paste from the two remaining chips, one NVIDIA GPU, and another Intel.

Also remove all stickers, foam, and plastic from the motherboard, as they will melt or catch fire in the next step

Pre-heat your oven to 395 degrees Farenheight.

Place the motherboard on a sheet of foil, on a baking sheet. Place into the oven for 10 minutes. Then remove and let cool

Re-assemble laptop following motherboard steps in reverse.