The short story is that all the G84 and G86 parts are bad. Period. No exceptions. All of them, mobile and desktop, use the exact same ASIC, so expect them to go south in inordinate numbers as well. There are caveats however, and we will detail those in a bit.
Both of these ASICs have a rather terminal problem with unnamed substrate or bumping material, and it is heat related. If you ask Nvidia officially, you will get no reason why this happened, and no list of parts affected, we tried. Unofficially, they will blame everyone under the sun, and trash their suppliers in very colourful language.
The symptoms are no video output but the computer still boots. After the problem occurs and you attach an extrnal monitor the system profiler lists the graphics card as an Intel X3100, instead of the GeForce 8600M GT that it should (pictured).
It's difficult to say what Apple will do, they've extended warranties for dud batteries, so its conceivable that they would something similar for this but they haven't yet acknowledged the problem, so who knows.
The Apple Discussion Forums are buzzing with the issue and someone has started a spreadsheet for affected users here.