I get a little bunch of laptop cast-offs for one reason or another. Often, if they are current enough to be useful, I'll track down whatever parts they need, within reason, and press them back into service with employees' kids for school or such. Usually I get Dells and have great luck with parts and well documented cures for their ailments. I even had one that required resoldering a surface-mounted chip with solder cracks.
The current one is a Toshiba Satellite 5105-S501 with a known problematic video card. Replacement cards are not available. The problem seems to be from too much heat and too many thermal cycles cracking the joints on the video memory chips.
On the Dell, I made an extension for a pencil soldering iron from 28 ga wire. It worked after three tries but it was like threading a needle with a baseball bat. I've seen reports of resoldering this video card with a heat gun at 750 degrees for a full three minutes. However, some of the people reported melting off the components and blowing them away. At that point you just scrap the whole machine. I'm thinking of making a jig to hold the parts in place or try again with the tip extension. I can't afford to spend any serious money on this but I hate to scrap the laptop just yet.