Don't believe everything a utility company tells you. Communicate with them in writing -- email or written letter. Keep track of all documents in this matter and consult with an experienced consumer rights attorney to see if there is a possible lawsuit for fraud.
The answer is most likely "no." However, the situation is much more complicated than that.
The three basic components of a contract are an offer, an acceptance, and an exchange of consideration (i.e., something of value). A "contract" requires the agreement of at least 2 parties. If your acceptance is missing, there can be no "contract."
However, there could still be a quasi-contractual situation if one party, for instance, were to accept goods or services from another -- in that case, there arises a legal argument that the party providing goods or services is entitled to a fair compensation for them. This is not a "contract" per se, but rather an equitable principle that says it would be unfair for a party to accept and use goods or services without paying for them.
Put simply, you need to contact an attorney in your area to figure out what, if anything, you owe on your energy bill.
My answers to the questions are for general informational purposes only and do not establish an attorney-client relationship. Accuracy of answers is not guaranteed, as my answers contain broad assumptions -- as such, you may not be able to rely on the answer under the facts of your specific case. There are no "one size fits all" legal solutions because even slight changes in fact situations may require a material variance in the applicable advice. Once again, I am not your attorney.