The battery should still be good after the first year. Perhaps the battery became loose within the player. Try opening the player up and resetting the battery by following these steps:
1. Turn the mp3 player over, so that the metal backplate is facing you.
2. Using a screwdriver, unscrew the four little screws on the metal backplate and carefully lift it off.
3. Carefully lift the battery out of the mp3 player and reinsert it, so that the battery snaps back into place.
4. Replace the screws and see if it turns on.
If it does not turn back on, the battery may be bad, or something more serious could be wrong. Try this out and see if it solves your problem.
Thanks! Resetting the battery actually worked! It turns on now! I guess it became loose somehow.