Well it's either the electricals on the compressor Relay, overload or the Compressor bit the dust working so hard when it was frosted over

Those little compressors won't handle much abuse. Like the bigger ones will. You can pull the relay off the terminals of the compressor if its a solid state style you can shake it and if it rattles its bad if its the plunger style where you can see copper wraped around a coil it will rattle. If it is more than 5-8 years old I would by a new one it would be cheaper than having someone come out and fix it or tell you the comressor is shot. You can pick a relay up any appliance parts store for about 25 bucks and see if that fixes it Your comprssor has 3 terminals on it that look like steel pins sticking out of it in a triangle pattern you have the common, Start winding, and run winding when voltage is applied to the start winding it powers it up then drops from the circuit and in a nano second the run winding gets power and it runs well if it cant start it just sits there and gets hot or burns up the windings