G'day and welcome to the forums.
I don't recognise that fault, but if you haven't found it in the instructions:
http://www.ricoh-imaging.co.jp/english/support/man-pdf/optio-wg2.pdf (This link is to the English version but there are other versions available) then hopefully somebody on the forums will see your post and drop by to help out.
I bought my WG2 new so it's approaching 8+ years old, and when seeing your post I pulled my camera out and tested the battery. It worked fine but I have found that leaving the battery in the camera tends to drain it more so now I store it separately. This is annoying as I have to manually enter the date/time info each time I go to use the camera but as this is a camera I use on occasion I'd rather do that than buy a new battery.
As you work through working out your problem, remember if it's only a battery you can replace the original battery through Ricoh (D-LI92), and there's likely to be some after market options around if you don't want to go with an original. battery.
Anyhoo, all the best, I've found this camera good for work and macro, as well as being a cool looking camera that comes with it's own carabiner. Especially if you have the orange one.
Tas