Okay, the 8800GTS is back in the system and it's now working fine *knocks on wood*.
I realize my mistake, with probably screwed up the card. There was a little power converter which converted the usual 4 pin, to a 6 pin (molex, I believe?). However, the first time I got this card, I only connect one of the two power supplies! That probably screwed up the card, with a too low voltage.
Anyway, after installing a bunch of crap from MSI and removing it again (thought I'd do this one by the book, but it turned out to be crap) I simply took the newest drivers from nVidia, and the card is now running okay. I hope it stays that way. Thanks for the help guys

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