What is wrong with my iPod?

I have a 3rd generation iPod touch. I got it last August, and since then I've used it pretty heavily. This weekend I accidentally cracked the screen, and then when I was in the middle f something like playing a game, or listening to a song, it started randomly powering down. And each time, I remember there was a full battery. Then when I turned it on it did that Apple logo thing on the screen, for like 5 minutes! It should normally be 1 minute. When it finally turned on and went to my screen saver, it powers off again! Last night, I was trying to turn it back on, it wouldn't! When I plugged it in to charge, it did that Apple logo thing again, for an unusually long time, then turned back off. Now it won't turn on! Does this mean my iPod's dying, and I should get a new one? Or can it be fixed? My warranty expires in August.