No, really, was there any progress since?
Now, let's assume that the backlight issue isn't because of the battery but some loose soldering somewhere.
The LED status issue however is something I do not like at all.
Might the IC of the new battery's protection board be the problem?
That being said, if you put the old battery in and start charging the watch, the LED (and who knows, maybe the backlight as well) might start working. If so, it's about the IC of the new battery, if not- then it's not.