If the compressor runs for about an hour and there is no frost on the evaporator/freezer coils then it is a sealed system problem.
This will be an expensive repair and often it makes more sense to put those dollars towards a new unit.

You can usually hear the compressor but also should be able to feel it vibrating when on.

It will not be a defrost problem because the fans and compressor are shut off during a defrost cycle.