Lightroom CC is not licensed with a serial number. You need to be logged into the creative cloud application manager with your Adobe ID and password when you first start Lightroom CC. After that, you only need to be logged into the application manager on a monthly basis so that it can be verified that your account is paid current. You might try logging out of the application manager and then signing back in and see if that fixes the problem.
Launch Creative Cloud and go to the Apps tab. Are you able to Open or Update?