So after much agony of dealing with my graphics card overheating (today it turned off on me while playing games four times), I decided to take the fan/heatsink off in frustration. So what I saw was an ugly little dried up gloop of thermal paste. The core seemed to be only about 1/2"-3/4" big.

My question is would cleaning the old paste off the processor and heatsink with that one type of alcohol, then adding new stuff like arctic silver 5 be safe? Also, would it perhaps fix the problem, or at least help? I remember my friends computer processor was idling at about 69C and then when he took the crap that came with it off and added new stuff it was idling at about 30C. Thanks for reading this post!

Well, you took it off so now you have to put it on. I wouldn't recommend running without it. Clean it off and use a THIN coat of thermal compound
Mark

The object is to only have thermal coating on the processor itself (that little 1/2" thing) - so very little is needed. Avoid excess! I put a dab on about the size of 1/2 a grain of rice and smear it around with my finger tip (then gripe and moan when trying to remove it from my finger tip!

Make sure the surfaces on the CPU and on the cooler are clean first!

Yes, I would find it quite safe. When I bought an aftermarket fan for my GPu, I had to put thermal compound or whatever you'd lkie to call it. But only put a tiny bit on the top where the name and such is. Like This. But maybe a bit more clean, you only need the most tiny dab.

Tutorial on applying compound:
Arctic Silver
Mark