Dried paste itself will not cause screen to go black or be dim, the only thing it could cause is the heat transfer from the chip to the heatsink to be non-optional and that in turn might cause shutdowns because of high temperature, which in turn might damage the video chip... but usually it just causes the temps to maybe be bit higher, I have this old PowerBook from 2005, never replaced thermal paste and it still works fine.
There has been many cases where Apple machines have contained excessive amount of paste straight from the factory which might be bad.
EDIT: If you have Macbook with Intel chip they also produce very little heat and therefore are not so prone to solder failure as Nvidias are. Of course even Intels do not last forever, but still, rarely fail.