From the sounds of it the control board may be toast.. By the way all is not lost.
On this system the ONLY thing the A/C has to do with the furnace is a single relay, this relay replaces the contacts on a thermostat, it turns the furnace on and off (NOTE the rear control system has this ability as well, it's just not wired in to the furnace since the wires go to the front.
Now here is the problem. The problem might be fixable, A full visual inspection of the control board and the wiring in the front unit may yeild joy
For testing: Go outside, access the furance from outside you may find a switch (Really a circuit breaker) on top of the blower housing.. TURN IT OFF, this kills the furnace (yippie).
Now you won't have dualing HEVAC systems, Restore power (12 volt) if the wires look good. inspect all the wiring and traces.. Good chance a relay is the culprit.. Theory has it you can find replacements for those..
If worse comes to worse you can try and find a new Carrier Air V control board, or a used one on E-bay.. Failing that I will have a spare come tomorrow.. However I really do not wish to part with it, I plan on keeping it just in cuss my other one goes bad.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times