Craftsman DYT 4000 won't turn over even with a new battery

I have a craftsman DYT 4000 that won't turn over even when I know my battery is completely charged. It seems like the starter doesn't have enough power to crank it. Every once in a while if I turn the key and then use my hand it will turn over to the point where it will start, but it used to start up just fine. If I turn the key for too long, the starter will start to smoke. Anyone know if I need a new starter or cylenoid? Or has anyone else had this problem. I just don't want to buy a new starter if it is something else.