Guess I don't know what you mean by "it sounds like a ground problem"- to me it sounds more like a dead short somewhere. "Ground problem" is usually that the circuit won't work at all- the opposite of the circuit shorting out and blowing the fuse.
Which fuse do you blow? Many circuits are activated when you turn the key to the crank position- you need to isolate which circuit is defective, then trace it down.
Another thing to do before getting too far into it is to remove the starter and have it tested.