1997 Mercury Marquis Auto Temp Control Unit VS Blend Door A

Air Conditioning problem
1997 Mercury Marquis V8 55,000 miles

Hello,
A/C problem-started as clicking noise from glove box area-than a/c went out-can hear compressor come on-but a/c blows hot air-heater still works.
Am getting conflicting info from shops-1 says ATCU-other says simply BDA and that other shop is trying to screw me because I am a woman.
Naturally want it to be BDA-I can find one and is cheaper. ATCU is discontinued, hard to find and costs a lot.
All info is correct, just not sure about engine size-whatever comes standard in "97 Grand Mercury Marquis
Read some articles that said the noise probably originated from a broken “helical gear" within the blend door actuator.
Appreciate any and all help-Thanks.