I recently pulled my old 6800gt out of storage to throw a HTPC together. I never had a problem with the card before, but upon installing the card, (tried in 3 different MB's I have lying around), there are artifacts (vertical white lines) consisting of dots that appear on the screen only through bootup, when it loads windows everything is fine, UNTIL I try to load a game or install the cards drivers. I know its more than likely toast, but it seems odd that some time in storage can do that. I also tried reflashing the BIOS to no avail. Is there anything I might be missing here??]
If there are fingerprints or other dirt on the card, try to clean it gently with alcohol or pure acetone. I suppose you already checked the heatsink and fan, although it doesn't seem like overheating problem.
You could also try to lower voltages a bit (like 0.1 V) using NiBiTor, and downclock a bit. I'm suggesting this because I remember my card had higher voltages during bootup and in 3D mode (I verified that with DMM).
Did you check the capacitors? If any of them is bulging or leaking or rusty that could be the cause...