Most generally a fan belt is tight enough that a person can turn an engine by moving the fan. Just don't bend a blade while attempting to do so. Should turn fairly easily.
I agree, I doubt that in this short of time period your engine would be stuck. Too bad that you can't just go out to check with the fan. Distance can be a problem for certain.
I question your term "electrical hum". Most generally a 6 volt or 12 volt auto system will not hum. Since I don't know your level of vehicle knowledge I'll ask, you do know what an unengaged starter running sounds like, don't you? Could it be that?
If the engine can be turned with the fan it almost has to be starter or starter connections.
Good luck.
