I have a bryant furnace with AC system. I turned the system on for the first time this year & it didn't run. We didn't use it at all last year, but worked fine the year before.
The 3 amp fuse on the furnace control panel was blown. I traced the problem to a short in the 2 wires between the furnace & condenser unit. Mice had striped the insulation off the wires for about 1 inch causing the short. I spliced the wire & the condenser unit now comes on & cools the house very nicely.

My problem is that the condenser unit never shuts off. I flipped the switch on the thermostat from cool to off. The furnace blower stops but the condenser keeps running. Could it be a thermostat problem? Any suggestions?

It could be welded together contacts on the outside units contactor.