It depends. What was that item listed as "carry out A/C service", which I assume is a work order of work they did prior?
Plus, I never did see what they said was the cause of the no compression, only the work that they did.
Was it possible that the fact that the cooling fan did not work that caused the engine to overheat and blow a head gasket, I cannot tell from reading that work order.
I think you should wait until the problem with the A/C and/or cooling fan is fixed, save all the old parts, ask for a more detailed work order and then weigh the price of what filing a suit and/or with a attorney against what you may gain or possibly lose further. But the main thing would be is to get it fixed, so you may even want to consider finding a different shop to diagnose the prior work, find out what it needs now, tell you why what failed and how much to fix it.
Tuesday, February 20th, 2018 AT 6:27 AM