The Home Warranty company should be no problem; they will look at the INSPECTION and the prolem now, and they should fix it: I doubt that you will get a new A/C, but you knew how old it was when you bought the house.
I have gone down to the City and had the utilities turned on in MY NAME so that we could do an Inspection; it cost me $85, (personally) but I got it done and protected my client!
The stove should have been discovered, and it is really your fault, and your Agent's, for not having the utilities turned on. Got a problem; solve a problem.
But that is still probably a $150 problem as is the shower leak.
Buyers don't realize that all the safeguards we have will not eliminate their due diligence: You cannot just sue somebody because of a $150 problem; and let me guess, the SELLER was a Bank?