What could be wrong with my iPod Touch?

I was in the car yesterday, when all of a sudden, my songs wouldn’t play anymore. I’d click a song, it would automatically be on pause or not playing, and then I’d click play and it wouldn’t play. I tried opening apps and they won’t open either, they close right away, before the app even starts up. I tried turning it off and on again, and it didn’t help. I can’t restore it, because I just installed iTunes on this computer, so my songs and apps (hundreds of dollars worth of content) aren’t backed up anywhere and would be lost. How could I possibly fix this? If we can’t fix it on our own, we’re planning on heading out to an Apple store to see if they can.