New job with Non-Compete Contract requirements.

I recently started a new job on a Monday w/ a new employer in the same field I was previosly in. I knew that I would have to sign a Non-Compete contract (NCC) in order to be employed by said company. I did not receive a copy of their NCC until that Friday. After reviewing the NCC contract and spending a week working in sales w/ my new employer I elected to terminate my employement. I promptly contacted my Boss on Sunday evening telling him that I would be resigning from my sales position w/ his company. He said that he wanted my company issued laptop to me immediately which I agreed. I met him at the office that same evening (Sunday) and turned in everything that was issued to me by this company. I did not sign the NCC contract. Upon leaving his office he informed me that he may elect to enforce the NCC. The company is a corporation of Kentucky but having this office in Mentor, OH. Does this employer have grounds to enforce this NCC even though I did not sign it? I'm just looking for free advice on this and am not interested in paying for legal advice at this time. Thank you in advance. Respectfully,