Battery dead or Starter problem?

Okay I drive a 1997 Chevrolet Suburban. A few days ago, it would not start so my dad jumped it and it worked again, but started with a little hesitation. We let it run and drove it about 15 miles I'd estimate. We had found a light (one of the visor mirror lights) was somehow staying on even though it had been closed. We taped the button that's SUPPOSED to turn it light off down, so now even when the mirror is opened it stays off. The next day (today, actually) it would not start, and it sounds even weaker than the previous days. My neighbor says it sounds like my starter is going, but I don't know anything about that. Before it fully died on me, a few random times my car would start with hesitation. Any help would be greatly appreciated!