Try this free webcam test site
. If you don't see yourself in the window after clicking Allow, then click on the camera icon below the window. A drop-down box appears. Look for your Logitech camera and select it. You should see yourself. If the Logitech is not a choice on the drop-down list then the driver is either disabled or corrupted. Go to the Logitech website, under the Support tab, Products, Webcams, and find and download the driver for your model of webcam. Once you download it try the free test tool again to verify all is working.
One more thing. Make sure your browser is closed when you plug in your webcam. Then when the browser is opened it will recognize the device. If the browser is already open then it might not recognize the webcam. Good luck!