Hello!
I have a Ti 84 Plus C SE that I was recently forced to re-solder the connector that allowed the battery to be connected to the circuit board. Everything works again but it got me thinking, why are there four wires coming from the battery? I'm assuming that the important ones are the + and - but do the other two even need to be connected?
Thanks!
One of the extras is probably a thermistor for temperature monitoring while charging, and the other may be some kind of identification or connection to some chip integrated in the battery pack. See also, "Why are there 3 pins on some batteries?"

It's also possible the two additional connections are together a communications interface to a combined protection/monitoring chip packaged with the battery, like a BQ27750 for instance.
  
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