The starter needs much more power than headlights, so this could be a simple as a discharged battery. If you have a battery charger, hook it up and charge the battery. What about your driving habits? Is the car used daily? Is the main use short trips?
Since you had battery issues a few months ago that old weak battery might have overtaxed your alternator to the point where it is failing now. Your new battery might not be getting a good charge due to a weak alternator, or just too little driving to keep it fully charged.