Xbee does not transmit when battery powered?

Hello, We are working on a project, that uses an Xbee remote sensor, that senses LDR data and transfers data to a Xbee coordinator connected to an arduino. The arduino after sensing data, sends a remote RF command back to the remote sensor that triggers an LED. I have been experimenting the remote sensor with a USB power supply so far.
Today, I thought of using a battery to power the remote sensor. I experimented with two to three NiCD batteries having 3.2 and 4.8V, by connecting it to the power supply socket in the grove board, but I see that when powered by battery there is no transmission received by the coordinator module connected to arduino. Transmission happens for a second and then stops, I set PL level to lowest for the remote sensor and checked again, it’s the same. Could you address this problem?
The second issue I faced was I had a 9V duracell battery for testing, and I connected it to the power supply socket, and it so happened, after 3 to 4 seconds, I removed the battery and tries powering the xbee board again with USB, now the xbee lights doesn’t seem to turn on. May I have damaged the xbee. The USB recognizes the board, and device is not identified in XCTU.

The grove board is not set up to be powered via the battery connection.

It sounds like you damaged the module as the Grove board if I recall does not except that high of a voltage.