What worked for me was to open it up, disconnect the battery, clean up any visible milk (a Q-tip and a little bit of water will work), let it dry, reconnect the battery, and then try charging it.

It's a standard 18500 li-ion cell, nominally 2300mAh. I can't identify the connector but it looks similar to a Molex Pico-EZmate.

The connector is shrink-wrapped onto the battery, and could probably be removed and taped onto a new one.