Have you checked the battery with a multi meter? Is it dead or just constantly low?
You most likely could rebuild the thing as long as you manage to open it in a "not too destructive" manor, however you may be able to find a battery at a better price then the individual cells would come to (ebay maybe?).
Personally I would try to rebuild it first - I used to rebuild batteries for handheld two-way radios (icom, maxon, relm...) for the sawmill when I worked at a radio-tv repair shop. 9 out of 10 I usually managed to get apart in a way that I could put them back together (the sawmill wasn't very prudent about looks as long as it worked). Gooped the cells up with silicone so they wouldn't rattle a JB welded the battery back together. Very often it was only one or two cells that went bad (I think it was usually the first & last in the serie). If the other cells checked out OK we would leave them and replace only the bad ones (bosses orders....), and the battery would often be good for another year (used pretty much daily) before another cell failed. This was only worth it because the radio batteries were grossly overpriced when bought from manufacturer.
If you don't have experience with electronics repair I can't really recommend trying it, after all, we are talking about batteries, with hazardous chemicals inside, with a potential for a fire or explosion if anything goes wrong. On top of that the cells will most likely be wired in some crazy series-parallel way...
If you go for it, please proceed with caution.
Dilly Bar Rob