The problem with the heat pump could be a wire burned off. Eight out of ten of my service calls have been just that; its very easy to sopt. Open the inspection panel and look for a wire with bruned insulation or an end hanging loose. In this case, I would expect the wire to be a compressor wire- the largest wires in the panel.
If it is not a wire burned off you could check the compressor for a grounded condition. With the power off, unplug all three wires to the compressor, use an ohmmeter touching one side to the compressor case and the other side to all three terminals on the compressor (one at a time), record the resistance at each terminal. Two of the resistance readings should equal the third reading, if this is so, there is no short in the compressor.
Try these two tests and post back, if necessary we'll talk about some other possibilities.