2010 Craftsman LT2000 Riding Mower Won't Start?

I have a 2010 Craftsman LT2000 riding mower with a Briggs & Stratton engine. It will not start. When I turn the ignition it either clicks a bunch of times or spins once or twice, but doesn't turn over. I replaced the spark plug, adjusted the valves, got a new battery, and it still won't start. I did notice that it is slowly leaking gas somewhere (will not hold it in the tank over night). I'm guessing my problem is either the starter solenoid, the starter motor, or a clogged carburetor. Any suggestions?