There are a few things I would note in your situation.
# How do you know it's short to ground? What is the actual resistance you ground you're getting? Many if the power lines that go to the CPU are naturally low resistance so this may be a normal reading.
# When any component on an electrical line is bad it has an effect on the whole line. So one bad cap would cause any component on that line to read as short to ground. It's like punching a hole in a hose. Doesn't matter where else on the hose you poke, it's still going to be leaking water.
No power on these can be any number of things, but it sounds like you're on the right track.