When capacitors fail they can fail open or shorted, in most cases they fail open - not allowing electricity to flow where it is needed.

I think I made a post long ago of even if you recapped and repaired a board, that it would still fail if the video and other cards needs recapping too. The caps on these cards are just as old as those on the mother board, and they would fail just as equally. And on some video cards I have seen, they have the same 47µf @ 16V caps that fails on most motherboards.