Battery indicator connected with bicolor led
You could use a MOSFET as a switch to do something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

So essentially, when the circuit is powered up, Q1 is on (it is a P-Channel MOSFET, the default symbol in this editor is a bit dodgy!) and so LED1 is on. When you connect the battery, it pulls the gate high, turns off the FET, which turns off LED1 and turns LED2 on. You may need to add a bit of extra circuitry, but the general idea is there and this should be a good starting platform to something a bit more ideal.

NOTE:

This circuit is not perfect, depending on your voltage supplies etc this may not work 100%, however, the basic idea is there and this is intended to serve as a general idea for the OP to work from.