The computer did it again, and since I was so shocking at describing what the problem was I figured I'd take a photo of it. This is the current array of screens we get while attempting to load up Windows.
So after seeing that, does my description of "all woobly and stuff" make any more sense? Due to the other symptoms the computer is suffering (very sluggish and generally ill) we are going to go with the graphics card being the cause and since berserkir has directed us to a reasonably cheap replacement we'll buy that and hope for the best. Thanks for your help and suggestions everyone. Greatly appreciated.