"....they seem to think that there is no problem with the graphics card (nVidia GeForce 8800GT)itself, which puzzles me a little."
They could be correct. It's certainly possible to have a graphics card which works in basic VGA mode (as during booting), but won't run at the higher resolutions after the OS loads. Safe mode, of course, also works in basic VGA mode.
I had one that failed in exactly this way, about a year ago.