I have a sears craftsman 18 hp mower. The mower deck will not engage. What do I check

Lets start by checking that the belts are in the correct place and tension is good. You do not need to start the motor, DON'T START THE MOWER just so you keep safe. Engage the deck handle and get between the deck and the engine using a flash light. The belt that travels arounds to all the blades and two other pulleys should be very tight. The belt going from the engine to main drive pulley on the deck should also be very tight. Check and get back to us tomorrow.

Good advice ball, only thing I would have done differently is to remove either the positive battery connection, or removed the spark plug(s). And yes it is not good to start the engine while inspecting. Good job.