The only other solution I could think of would be to remove everything Logitech from the registry. I just downloaded a little app called RegScanner (downloaded the 64 bit zip and extracted it to a folder on my desktop). It runs from the RegScanner.exe. I typed in Logitech and it came up with about 950 registry entries. I remembered I had installed a Logitech game controller on my computer at one time. I suppose it would be safe to remove those entries because it is not part of Windows. You would also want to remove the hidden ProgramData file for Logitech on your C: drive and any program file entries and hidden AppData entries under your profile. For the AppData and ProgramData I have had to use the take ownership program to get permissions to remove it. HOW SAFE IS THIS? Maybe that would be a good topic for discussion. I would certainly make an image of your hard drive and be ready to use it just in case. Have I done this, YES but only in extreme circumstances for repair where a program reinstall is critical. A restart would be necessary afterwords before attempting a reinstall of the program. Your symptoms indicate registry corruption for that program.
I have removed everything that had any reference to Logitech from the registry. booted up. problem was the same. I did a clean install of windows 10 and I have installed the Logitech program. Thank you for your replies.