how much for a new air conditioner

To answer that bluntly...$$$. Just guessing I would say no less than $1,200.00

You don't need to replace the entire system. It needs to be tested to see if the Compressor is working (The clutch inside can be worn out after this many years), and if it is, you need to find out if there is a sensor, or switch issue. You can get a used acura cl hvac control module and computer(Part # 79650-SY8-A01 & 79610-SY8-A02) sometimes come used together, a new SENSOR, EVAPORATOR (Part #80560-SV4-A41), for under $120. It is a process of elimination, and Honda/Acura cars are notorious for their sensor issues. You need an independent, honest mechanic that can narrow things down. There are 1,000 of used parts that cost a fraction of what they were new, that will work just fine, and make the repair cost effective. Good Luck, and be patient.