Generally, the statute of limitations for an oral contract is 2 years. What becomes interesting is whether the other party uses the transcript, in which case an argument can be made for promissory estoppel (i.e. although there is not a written contract, they would be estopped from denying the existence of the contract).
If you followed up with invoicing, then you have an account stated, plus other common counts, which can be for four years depending on the circumstances and what responses, if any, you were given by the other party.
This seems like an oral K if no other writings were involved. That said, even if 2 years have passed, when was the breach? Surely it was not at time of billing. Maybe the SOL is stayed a while...
It looks like there may be potential arguments to make regarding when the breach actually occurred or the nature of the action(s) available for recovery. You need to do a bit more analysis to determine if there the SoL has run.... Consider discussing the specifics with an attorney to pin down a course of action.
**Nothing in this response should be construed as legal advice. The post is for general informational purposes only. This information is not intended to create, and receipt or viewing does not constitute, and attorney-client relationship.**
THIS IS NOT LEGAL ADVICE. INFORMATIONAL PURPOSES ONLY. Legal matters are like thumbprints, no two are identical. Therefore, you should discuss your question with your own attorney or if you do not have an attorney, strongly consider hiring one. The information in this posting is for general information purposes only. No part of this posting should be taken as legal advice for any individual case or situation. This information is not intended to create, and receipt or viewing of this information does not constitute, an attorney-client relationship.