These batteries store up to 4.2V; voltage will drop with normal use. Most devices will stop working at about 3.3V, for having the batteries overdiscarge may damage them. 3V to 2.85V is often safe-ish. 2.6V means no good news.
If your LDK works without issues while plugged to an USB charger then the problem will either be in the batteries or in how current is drawn from the battery to the device. If you could test the batteries with other devices (or a multimeter) and see those are ok, it'll be great; positive is to the edge of the battery, negative to the center, middle was used by phones to monitor the batteries. Next, check the device battery contacts: three metal loops that touch the three plates in the battery. Check they're well aligned with the battery plates, not twisted of warped. If those are ok it might be a bad solder or a short inside the device. I hope it's not that.