i would say that is the case then , the 8600gt has overheated.
replacing the fan will not fix the issue , it will need to be replaced anyway but that logic board will need to be replaced or baked in a oven(sounds crazy but its worked great for me) to repair the video chip, i wouldn't recommend that route unless you know what your doing.
since fans are cheap(ebay 10$-15$) you can replace it and see if it can hold up.
good luck,