Hi there liquid, I had the same prob with my ipod a few months ago the battery would only last less than an hour, I bought a brand new one with the little tool to open the pod and think it was around �12 for the 2, it was a little hard to get the case of but once you do it is quite straightforward to replace the battery and the case goes back on a lot easier than it come of.
And my ipod is like new now .
Just realised you said you had the ipod video (you lucky lucky person) I peplaiced mine on a poor persons that just played music loll.
But I assume the procedure is the same for the video ones if you go on e bay and find a seller that specalicces in the ipod batts then they will help you out.