I have a 16 year old Trane XE60 AC/Furnace. After a large storm the blower fan will not turn off. I have even disconnected the thermostat to eleminate that.

Relay Contacts MAY be fused. If you remove a control wire from Fan relay and it continues to operate, replace Relay/contactor.
Reconnect thermostat the way it was.

If you have a printed circuit board inside the furnace the blower will run all the time to let you know you have a problem. It may just be a fuse blown on the control board(5 amp automotive fuse) or a open limit switch- roll out limit on top of the burners or vent limit around the top of the unit on the vent pipe.