Thanks, I'll try that next time. THIS time, I decided to reboot and then delete the C:\Program Files\CCleaner folder. I tried to delete it before rebooting but it wouldn't let me delete a file or two. So as I was going to reboot, I got the message saying that "other people were logged in" and, since CCleaner runs in the background, that's why I couldn't delete the files.
When I rebooted, then deleted the files and folder, I was able to install the new version!
Problem solved!