You ultimately did give notice that you were moving out (er, that you had moved out). Your landlord can charge you expenses to the extent consistent with state law for removing your stuff or having to change the locks because you kept the key, but your failure to return a key doesn't renew your lease.

You appear to have been a month-to-month tenant, so normally you would be liable for rent during the notice period required by law. In Utah that appears to be fifteen days.