I would still suspect the battery as not having enough charge to turn over the engine. Batteries should be kept on a trickle charger if not used for over a week. The older the battery, the more likely it is to fail. Once a battery has been discharged then it suffer damage and be less likely to hold a full charge again. Lead Acid batteries work best when kept fully charged and not discharged below 80-90% of full charge, Lithium batteries can take more discharge before suffering damage.
If a new battery doesnt solve the problem then check battery connections and then maybe wiring from battery,ignition and starter button.