Welcome
Just a little thing to start with.
We have nothing to work with but your words so the actual words you use are important
Crank = revolve
Start = goes bang a few times
Runs means it goes for long enough to start cutting grass.
You have a problem with the PTO Switch , the parking brake switch or the wiring between the switches and the coil .
Until you tell us exactly which Troy-Bilt mower you have this is as much information as I can give you.
We need the numbers off the tag under the seat128