Starting

I bought the car on Saturday fired up first time, been using it for a couple of days, no trouble, really happy with my purchase. Then yesterday it refused to start, sounded like a whirring noise and if I was to take a guess I would say the starter motor was not engaging correctly. I started it a few times after, with my luck varying between success, a bump start and a jump start. I left it alone over night and it fired up again this morning. Is it likely to be the starter motor? Or I suspect it could be the battery? It had been sat for around two months before purchase.