>"Putting the GPU into an oven and baking it for a while fixed the problem for a few days by resoldering cracked solder points, but then it returned. This is probably related to the switch to lead-free solder in 2006, which is more brittle."

no, no, NOOOOOOOOOOOOO

Nvidia makes faulty GPU chips for 9 years now (underfill between die and bga carrier package). Starting with G84, up to at least Fermi, EVERY SINGLE GPU will die from thermal stress is used extensively at high temps. This is very well documented in numerous lawsuits that forced Nvidia, DELL, APPLE and other manufacturers to do repeated expensive recalls.