First off. Are they both USB devices?
I seem to recollect having a problem with a logitech Webcam and various HP printers in the past. One line from the Webcam installation instructions I can remember was to remove all other usb devices from there sockets before installing the webcam. This also happened when my old Mustek scanner was connected and we installed the W/cam . took a while to figure out but we did eventually get it all up and running.
Sorry I can't be more precise. BUT maybe my reply will fire someone else into helping.