One of those strange things. I know that Microsoft's Update is up and running again. Was something new installed?
I have a Logitech c270 and tested on webcamXP/5, 7 and on NCS with no problems. Logitech is usually very easy to work with.
Stupid question, but of cause you have disconnected/connected the camera and started the software again.
The other thing is if something is wrong in the configuration file for the camera in webcamxp. When you uninstall webcamxp make sure that the folder for webcamxp is removed from the library C:\ProgramData\webcamXP 5 and in Program Files (x86). Install and connect again.