As far as I have been able to find, this sort of problem is either the cpu or the graphic processor, to fix you have to reflow the solder.. problem may be fixed by just cleaning out the old thermal compound and reapplying but only if the solder is intact.. and if you have the machine open you may as well reflow the solder while your at it.. I have read and watched so many vids on how to do this and still haven't done it yet. I know they recommend using 'no clean flux', but before doing anything remove the PRAM battery clean everything well, clean off old compound with isopropyl alcohol.. and if this doesn't work then I don't know what it could be..
I'm sure someone more learned in this field would have the answer.