Once paired to Lichtnarre, I am able to do the calibration and then use the wiimote as a mouse on my desktop.
This probably isn't all that helpful, but once you have reached that point, anything which happens after that is not specifically related to Lichtknarre.
Something on the system is interrupting the relationship between the controller and the LK software, be it a third party utility which might be waiting in the background to launch with whatever app you are starting, or the app itself. Basically, anything which hooks controllers to read them directly, even if it is not specifically geared toward BT devices, could interfere with LK's communications.
You stated that you have used other similar drivers/apps on the system prior, so my question is how much of the code from those is continuing to linger on the system, possibly even after an uninstall? By their nature, some of these kinds of drivers use code which digs deep into the lower rings of the operating system, like at the kernal level, and might be difficult or even impossible to remove without a special piece of software specifically designed for that task, which would need to be provided by the developer.
Or, it might just be a silly configuration error for whichever application might be causing the issue
It's hard to know, but if fiddling with app configs yields no success, it's likely going to be something much more difficult to figure out, given the other software you had running previously on the system.