As a standard 'rule of thumb' procedure on such electronic faults, I would open up the unit and look for a cracked intermittent solder joint or connection. You may get it to work cold by gently flexing certain components or the circuit board. If so, then try to localize the area and check all the solder joints.
An audible hum is usually generated by a power transformer. It may be loose, which would explain both anomalies. An audible hum in the audio output usually means the filter capacitors are dried out and need to be changed.
Sometimes components like transistors go thermally intermittent but its usually the other way around, meaning it would work until it gets warm enough not to work. In that case bench techs often place a desk lamp or heat lamp over the unit until it stops working then use a freezing spray on each suspect component until you find the one that makes it work again.
Without seeing the unit, I'm guessing that you may find the power transformer may be loose.
