Sarge, as the fan runs, but the compressor does not, the thermostat may be defective. I fixed this by consulting the maker's website for a wiring diagram, cutting the wires to the internal thermostat, and installing a wall-mounted digital thermostat, which, in any case, is a great improvement. To avoid the possible waste of buying a thermostat, only to find there is another fault, just shorting out the two wires to the internal thermostat would test the idea. Details of fitting the external thermostat are here:
I'm assuming you have an internal thermostat. If you already have an external thermostat, then you can just short across the wires leading to it. The usual safety caveats apply.