What should I check
Check your battery terminals. Then check them again. Then clean them just to be sure.
Check the Big red hot wire going to the starter, make sure it's not loose or damaged.
Check your motor ground. (this would also make the engine stop running if it came loose.)
If all that's good, and it doesn't work, there should be two wires going to the starter, one small, one big. With the battery hooked up bridge these two with a screwdriver. PREPARE FOR SPARKS and the motor turning over, and don't kill yourself. You're hotwiring the starter. be careful not to bridge from the big wire to ground, not if you value your screwdriver. (or eyesight for that matter.)
If all you're getting is a click at this point, check to see the starter is bolted up tight, and if it is, your starter probably took a dump.