2003 buick lesabre

This could be a longshot but I have an issue with my 2003 lesabre limited. bought it from a friend and they said that the battery used to just drain every night, they ended up unplugging the radio fuse and it stopped it. he mentioned that it would babble something about entering a phone number...

When I'm driving, My car started rumbling, just kind of bouncing / rumbling even while I'm sitting still. I can even see my grocery bags in the back seat shaking a bit even while I'm at a red light. Been over a week. All fluids are good It's a 2003 Buick LeSabre custom. Does anybody have any ideas?