I did send in the GPU and had it repaired in California, by http://stores.ebay.ca/brickfence.
Not just a reflow, but had a new chip installed on the GPU, came to about US$ 140.
After that I needed to replace the HDD as well. Since this model is very touchy about what HDD it wants, I needed to order a conversion kit for about US$40, so it now allows any old HDD, including even 2.5" SSD. This concludes my fix, she is up and running smartly now, for hopefully another decade.