Maybe there's just enough time to catch 1 digit, get someone to do this with you so you have 2 sets of eyes on the job, but try and get 1 digit at a time by just sitting watching like a hawk and writing them down, using a finger to mark your place, and constantly letting it boot and reboot until you have it all.
One other option that would work is if you had a LCD TV, with a frame freeze button, like freeze the BSOD screen onto the LCD and take note - might take a few tries but it's one option if your TV can deal with that.
Really you either get those digits or blindly reinstall XP, there is no way to fix the problem without those digits, save for reinstalling of course.
I would guess that the issue is caused by a GFX card problem, perhaps you PC is even a little under-powered for the card. For instance nVidia cards all seem to love power, don't give them enough and there's trouble. What WATT power supply are you using?, also how is the GFX card powered? - does it have power inputs for HDD power cables?
If you've bought the card and installed it yourself, there may be a PSU problem caused by the amount of power the card consumes. It's one thing that comes to mind, especially as the whole thing is crashing, BSOD included. I'm not sure now, that a corrupt file would kick out the BSOD, usually it's dodgy hardware that does stuff like that. I have a friend who just had to upgrade their PSU to suit a new 8800, so I'd watch for that.