Help, my 1994 Subaru Legacy won't start?

I have a 1994 Subaru Legacy, and everyone is boggled because 99 times out of 100 it will start, but then that 100th try it won't. I have purchased a new battery, and had the started and alternator tested, and both were good. My grandpa, thought that it was a result of the ground connection so he made a direct connection and still every now and again, it won't start. It will crank but won't turn over. If I keep trying it, or wait a few minutes it eventually starts, but I'm boggled. It's getting to be a pain, and I think I'll eventually damage something further. Please help in any way you can. Also at times my car will stall, it will act all choaked up and just shut off. I don't know if this has anything to do with it not starting?Any help is so greatly appreciated.