Although the BCR2 appears to be working, I would also try replacing it with a new MTH battery. I had a board that just didn't like the BCR for some reason.
The fact that you hear a click at power up is a good thing. It's not responding so I usually find out what address is stored in the board. If it reverted back to an old address, or obtained a new one, the remote maybe not talking to it for some reason?
Dead batteries get this issue. So I'd lean towards the BCR.
When you press read on the remote with only this engine getting power on your layout, does a different engine come up? If so, press start up and see what happens.
You stated that the remote recognizes that it's actually on the track and it becomes active?
did you put it back on the test track and verify that it still worked?
