I believe there is a safety switch that blocks the
tub from spinning when the lid is open. It probably burned out a switch
due to the lid being left open.



I doubt it. That switch just opens up the circuit, thus no electricity
will flow.
What could have happened ( and this happened to me) is that during the
agitation, the motor somehow got stuck or ceased, overheated and
tripped its internal thermal breaker. After a few minutes cooling off
the breaker will reset. This happened to me once and has not happened
since. I don't know what caused it.
If you want try jumping out the lid switch to see if it works again.