You may have a wiring issue, such as a loose connection or a damaged or broken wire. Take some time to trace and inspect your wiring through each safety switch and/or other connection, and to ensure connections are sound, throughout. this is relatively simple and there is no expense except your time, and it’s possible you might find and easily correct the problem.
Don’t know what kind of mower you have, but most use a couple of switches to ensure safety before operating the mower. For instance, you have to be on the seat, and the clutch has to be depressed, and the deck has to be in the up position, etc., before the mower can be started. And, the mowing deck itself must be lowered before you can start the mowing action. Considering you said a belt must be in place, as well, in order for the PTO to engage, there must be some type of switch used there, also.
Generally, most Safety switches are tested with a multi-meter for continuity to ensure they’re working.
Hope this helps. If not, add more details about your mower (mfr, model no., etc) and maybe we can come up with something more specific.