I just went throught the failed Nvidea 8600M GT GPU chipset thing with my Late 2007 MBP two weeks ago today. CMCSK's link will show that the Repair Extension Program (REP) covered from four years from date of purchase but was shut down on 7 December 2012.
It did not apply a Late 2008 MacBook Pro unless you have the 17-inch, which retained the pre-Unibody design. It was for MacBook Pro with "3,1" and "4,1" --the 17-inch late 2008 MBP was a 4,1.
Being willing to pay something to get the old MBP fixed, I also asked Cupertino about a flat-rate "Depot" repair but was told they no longer had parts form mine. As yours is a year newer, you may have better luck.
I now have a new 13-inch MBP to succor my sorrow.
OK so what I would recommend i that you just let it fail. When it does what you do is plug it into the wall, turn it on, and as it is booting, close the lid, wrap it in a thick quilt and put it upside down. Next you let it 'cook for about and hour. Once you do that you let it cool completely and turn it on. Then it should work.
I can attest to this as i had the exact problem, the computer died and wouldnt turn on any more, but this method worked a charm, I'm typing this on it right now! What you basically do it the same as reflowing the GPU, this is a fancy term for basicalle baking the gpu until it works again, but this method involves removing the logic board, a very tedious process. The quilt method requires aquilt, and an upside down computer. This IS NOT a permanent fix, but it could last up to a year before it goes again, in which case repeat the method! Hope this helps!