Ipod classic was doing "charging please wait screen", wouldn't charge, and now appears to be dead. Could this be the battery?

My 80g iPod classic was working fine, the battery wasn't draining unusually quickly and my computer was recognizing it, but I plugged it into my wall outlet last night, the one I charge my iPhone with, and when I checked on it later, it was displaying the yellow triangle, low red bar, and charging please wait screen. I tried plugging it into my computer and it wouldn't show up in itunes and the "charging" screen flashed periodically but never improved. This morning I tried plugging it in again with a different chord and it only appears to be weaker as now the charging screen only appears when it is first plugged in (I have tried leaving it plugged in for a while too). I did notice that when I initially plugged it into the wall charger it displayed a full green bar (rather than the growing green bar) and said charged, despite that the screen had showed that the battery was below the 50 percent mark. I thought, at the time, that maybe the wall device just charged differently and I hadn't noticed before.

Is there any chance this might just be the battery? I have had and frequently used the iPod for about 4-5 years now, so it wouldn't surprise me, but doesn't a dying battery usually manifest itself by weakening significantly? I was still getting hours whereas I've heard near dead batteries won't hold more than 15 minutes sometimes. The only other thing I could think of is that I'm a runner and it's been a hot summer. I lot of sweat has soaked into my armband and appears to have corroded some of the edges around the iPod's frame, near the metal. I wonder if this could have damaged it somehow, maybe gotten through the USB port or something. Has anyone else had this experience with their pod? I would be thrilled if I could just replace the battery, but I don't want to put money into it if it's a lost cause. Any insight would be appreaciated. Thanks.