I don't know how the laws differ in various states, but in the state of California a successor has liability if:
(1) the successor expressly or impliedly agrees to assume the subject liabilities,
(2) the transaction amounts to a consolidation or merger of the successor and the predecessor,
(3) the successor is a mere continuation of the predecessor, or
(4) the transfer of assets to the successor is for the fraudulent purpose of escaping liability for the predecessor's debts.
You can try to sue in small claims court for damages. While a small claims court judge may award you damages (I believe small claims runs up to $10,000), he/she has no authority to force the company to honor the warranty.
From your description, the question here is whether or not the lifetime warranty policy truly was in place in '84, or whether it did, as they claim, only begin in '86. You may need to do a little more digging into the company's history for that one.
Hope this helps!