Hi,
The A/C compressor has a pulley that has an electric clutch. It engages when the compressor is signaled to turn on. When the car is off as well as the belt, you should be able to spin that easily. If the compressor itself has locked, with the A/C off, the belt won't be able to turn the compressor. With the belt off, you won't be able to turn the compressor clutch pulley.
As far as cost, if the compressor has failed, the system may be contaminated and require other components to be replaced and the system flushed. So, it can get expensive.
I don't know where you are located, but around here, I would expect this to be around a 700-dollar job. But that would be based on what actually happened.
As far as replacing the compressor, here is a link that shows in general how it's done. Take a look through it and see if it is something you feel comfortable doing.
https://www.2carpros.com/articles/replace-air-conditioner-compressor
Let me know if you have other questions.
Take care,
Joe
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Tuesday, August 2nd, 2022 AT 10:27 PM