Starting system problem

Please help. I have a 2000 cadillac deville w/ about 60,000 - 70,000 miles. I had it put in the shop a month ago and they said it was my starter. They put a new one on and it still wouldn't start so they ahd it towed to a cadillac dealership. They said it was my motor ground. All went well for two weeks. Then the problem reoccurred. The cadillac dealership then said my new starter was bad. So they put another one on. I got it back two days ago and guess what? I'm having the same problem. Sometimes it clicks w/o starting or sometimes it won't do anything. I don't know if this is much help but sometimes my car accelerates on its own. I don't have to put my foot on the gas and it will speed up by itself. Please help.