If your micro:bit does not appear to power up when connected to a battery, there are a few things you can check:

If you have the latest BBC micro:bit, it has a red power LED, that will be lit when on USB and dimly lit on battery.

If you think there is an issue with the micro:bit, try the following:

1. Check your batteries work. Try them in another device, if they don't work, replace with some fresh batteries. You can also measure battery capacity to ensure you have enough power to run your program. 

2. Check the black and red wires that run from the battery pack to the white connector that goes into the micro:bit, make sure there is no damage to them and that the polarity is correct (some JST connectors can be wired in reverse). The red wire going into the terminal should align with the '+' symbol on the silkscreen and black with '-'

3. Check that the white JST connector that plugs into the battery socket of the micro:bit is firmly pushed in.

4. Check when you plug your micro:bit in via USB that the USB activity LED on the back lights up.

If none of these steps help to solve your problem, it looks like your micro:bit might have developed a fault. You should get in contact with the company that you bought it from and check what their returns procedure is.

The USB activity LED does not light up

This is normal behaviour. The yellow LED on the back of the micro:bit will not light up when only running from batteries

The USB Activity LED is powered from the KL26/KL27 interface processor (the chip that manages the USB interface on the micro:bit). When powering the micro:bit using  a battery pack, the interface processor does not power up, and the USB activity LED will not light up.