'8600': what a disgrace.
Yes, it's most likely the graphics card. Potentially every 8600(M?)-based laptop (including those with high-end Quadros) will be affected. I suggest looking into getting another machine; one day your current one just won't boot.
The trouble doesn't stop there: certain 9600M-series ICs had the same issues, so I'd stay away from them also (if looking for a second hand machine).
Note also the repair services (commonly seen on eBay) are just temporary solutions. I sent in a 8600M-based MacBook Pro to have it's GPU replaced/resoldered. All they did was heat up the logic board in an oven to reflow the solder. The machine worked fine for a day or two, then problems started reoccurring. Even a new logic board from Apple wouldn't have solved the problem.
I am very frustrated about this having had two fairly high-spec laptops fail. The 8600M was a great chip; the last thing I would have expected is poor solder quality control from Nvidia. For a few years after, I went on a Nvidia strike.