Did you get any results with Strollin's advice?
I don't know much about your laptop, but the little research I did suggests that yes, your graphics is indeed discreate and removable. In addition, I found a few articles that suggest that those GF 7900GTX Go's were renound for failing
. I'm not sure where you'll get a replacement though, as the laptop is a tad old and rather unique. Ebay is perhaps your best bet. As for the price of your part, I have no idea, but I'd hazard a guess that it would be quite shocking.
What could you get on ebay? I wouldn't say much more than ~£45, if that. This is because in the grand scheme of things, it's very outdated. It doesn't work. It isn't in high demand. It's old and not very portable. Perhaps breaking it up would get you a little bit more, but then you'd have to weigh it against the effort and ebay listing fees.
Personally, I'd forget about repairing it unless you get a hold of a replacement graphics card, once you've confirmed that's the problem, at a decent price. A dual core Pentium chip based on Core 2 archietecture would be much faster and HP do laptops with them for about £300 with 3GB of DDR3 RAM, a fresh warranty and in some cases, ATI - better than Intel Integrated - Graphics. An Intel i3 could even be in reach for a bit more. I'd seriously think about a new laptop along those lines over considering paying the $400 to $500 dollars the Geek Squad are asking.