You can sue the home inspector for negligence, which is the failure to exercise due care (that degree of care that a reasonable home inspector would have exercised under the same or similar circumstances to prevent foreseeable harm). Your damages (monetary compensation you are seeking in your lawsuit) for negligence would include the foreseeable costs you incurred caused by the home inspector's negligence. If you can prove that the seller knew and did not disclose  that the HVAC did not work, you can sue the seller for fraud. You would file one lawsuit naming the inspector and seller as defendants.