I bet the loud hum is DC voltage on the speaker. Measure DC voltage with your meter between the two speaker terminals. It needs to be about zero. If you see 15v or 20v or something then the amp has a blown output.
See the five-leg thing bolted to the aluminum finned heat sink in the center? It will have a number on it, probably TDA2030, 2040, 0r 2050. That is likely bad.
Other possibility is broken solder on the main filter caps. Those are the two blue cylinders just above the heavy red and green wires, left of the aluminum heat sink.
other things could be, but those are most likely.