Ipod Trouble


I have had this ipod, my first, for a little under a year, and there have been no problems... until now. I actually have two problems at the moment, one big, one not-so-big:

First (the big one):
My ipod does not register on my computer anymore. I connect it, and the screen on the ipod changes to that "DO NOT DISCONNECT" Warning. But nothing happens on the computer. Itunes says that there is no ipod connected, and the icon doesn't come up on the desktop. Then, the only way i can safely disconnect it, since there's no way to eject an ipod that's connected, i shut down the computer, then disconnect. I don't understand. What am i doing wrong?

My ipod battery has all of a sudden stopped lasting as long. The battery on the ipod get to the half-way mark, then it says low-battery and shuts down completely until i can re-charge it. Is there a way to fix this? If not, can i get a replacement battery for free? Will i lose all of my information if i do?

Help Please.

Thanks in advance,