The "we're not liable" language does not automatically end the conversation, but whether it holds depends on how the clause is written. A blanket limitation-of-liability clause is enforceable in most states, but a clause that tries to waive liability for the vendor's own negligence gets scrutinized harder, and some states will not enforce it at all for physical damage caused during active work. The crack defense is the oldest move in the book, and it only works if they can show the defect predated their work. If you have timestamped photos from your walkthrough before they touched anything, that is the evidentiary gap they cannot close with a verbal claim.
The practical path is small claims if the radiator's replacement or repair value sits under your state's threshold, because attorneys' fees on a dispute this size make any other route economically pointless. Before you file, send a written demand that cites the specific clause you believe their negligence overcomes, attaches the before photos, and names a dollar figure. A lot of vendors settle at that stage because small claims court is an afternoon they cannot bill to anyone. The number I would want to know before advising anything further is whether you got a written scope of work before they started, and specifically whether it addressed pre-existing conditions or required them to document damage before removal. That document, or its absence, is what changes whether your photos are conclusive or just one side of a dispute.