I have a similar problem with 3D Vision glasses, and a dead battery. These are LiPo batteries as well.
Based on my reading and understanding of batteries (EE background, not totally guessing. :s) you should be able to replace the LiI/Po battery there with something used for RC planes. All the batteries are very similar, the 3.7V is the key.
Do not under any circumstances replace the battery with a coin-cell or anything not LiI/Po because there is a charging circuit there that will interact badly with non-chargeable batteries. NiCd, NiMH are the wrong voltage and will not work.
It's possible battery itself has a circuit board, that's how the 3D Vision glasses work. But your description of the tabs being soldered to the board itself suggest that it's a stock LiI battery, and that the overvoltage protection is provided by the headband circuitry. This is what I would expect design-wise.
Here is a post regarding battery replacement in the glasses, and has some detail about sourcing the LiI battery.
I think Martinus nailed it with that link above. You should be able to just solder a new one on the board.
In terms of soldering in a new battery, that is going to be very easy for someone with a little experience. Without experience, you'd be better off to find a local tech-shop of some form, or DIY group, or MakerFaire type people who can do this in their sleep.