This may help:

OR if you're not a Gallifreyan Level Physician, here are some steps that worked for me when my Logitech 9000 acted up:

1) Unplug the camera.
2) Insert the QuickCam v11.9 CD. (Note - Hold down the left Shift key to temporarily disable the Windows Autorun feature.)
3) Open "My Computer", then navigate to the CD "Drivers" folder.
4) Double-click on the "LgDrvInst.exe" application. This will copy the camera drivers to C:\Program Files\Common Files\LogiShrd\LogiDriverStore\lvdrivers\11.90.1262.
5) Once the camera drivers have been copied to the system, the application should close. (Note - A reboot *may* be requested at this point.)
6) Plug in the camera.
7) The Windows "Found New Hardware Wizard" should start, and the Logitech hardware drivers should install.

Then:
1) Unplug the camera.
2) Insert the QuickCam CD. (Note - Hold down the left Shift key to temporarily disable the Windows Autorun feature.)
3) Open "My Computer", then navigate to the CD "QuickCam -> x32" folder.
4) Double-click on the "QuickCam.msi" application.
5) Once the camera software has been installed, the application should close. (Note - A reboot *may* be requested at this point.)
6) Plug in the camera

Hope this helps.

Is the webcam working with another computer? It may well just be that the webcam itself has broken.

You should go to logitech forums/website and contact their support.

Solution:
Delete System32, then reboot.

Try it on another PC, if it doesn't work, it's the webcam itself that is broken, likely wire frays, it happens a lot to webcams.

Had the same problem and I read online (well it must be true if it's on the internet xD ) that it can be malware or something like that causing USB recognition issues. I spent a whole day trying to fix it and in the end reinstalled the whole OS and it worked like a charm xD
If you can't find a way to fix it just back-up files and do a fresh install

Stay safe!