My 18.5 Rider Troy Bilt Tuffy will turn over but will not hit. I put a new battery, air filter, starter relay, and new spark plug in it. Checked gas going to carb but still will not start.

Did you try pulling the plug out after some light cranking to see if gas is making it to the top of piston? (is the plug wet or smells like gas?) Second, are all of safety interloacks working, deck clucth disengaged ?
You can attempt to check for spark by pulling plug and setting on grounded engine metal and trying to start. Do NOT touch plug, you will get shocked.