Your original idea of changing the motor was a likely culprit given the description you wrote. Not super common on these but it the motor thermal safety opens it would take a little while to reset. 45 minutes seems long for that however.
1st verify that both sides of the breaker are properly closed, some breakers will allow one leg to be tripped while the other is closed. It is a quick basic check that still bites me in the butt once in a while.
It's time to look at electrical issues. So you need to verify that the motor is being powered by the timer. Look for 120v to ground and neutral at both sides of the thermal fuse if you have easy access to the back and are ok with testing live. You can also run these with the drum out as there is no belt switch so you can look for voltage at the motor terminal block also.
I believe the timer provides neutral and 120v to the motor, if you don't see 120v between neutral and hot at the motor start tracing it back. Don't rely on 120v to ground as that is not what the motor uses. You can also check this at the timer.