Well that's great news for you, maybe was another charger for the Pro Back or another product. 3 pin Li-Ion are often Positive, Neutral and Temperature or Sense.
Temperature is often measured via resistance (often a few K ohms), you can easily check that with a multimeter, get a reading at room temperature, then cool down the battery on the fridge and see if the value changed, also if it's temperature you can see the value modifying as it warms again.
Sense is often a fixed resistor, different resistors means different things, like full battery capacity and such, somewhat an identifier.
In some weird cases the third pin is a serial communication line, since the charger is so simple and the replacement batteries looks quite cheap (i have one on mine) i don't think is the case.
I'd try to supply voltage to the camera and see if it works, for testing purposes a lab power supply is really good to tune the perfect voltage and limiting the current in case something goes wrong, but with a regular 12v power brick and a cheap variable dc-dc you can make your own test power supply. if you read 7.8v that's perfect for two Li-Ion cells in series, they go from 3.6v when almost discharged to 4.2v fully charged.
As a source for batteries i like to go with good original cell phone batteries, they are much better than regular cells from disputable sites and they tend to be cheap if it's from a model that's somewhat outdated, on my NC2000 i have an assortment of really old cells from the mid 2000s and they work really well, for another project I used some NOS Blackberry batteries for the Q1, those are made in Japan and they've taken a beat without a significant lose in capacity (actually i think what they are powering stand on the same amount of time since i build it).