PS CC shouldn’t ask for a serial number because it is licensed by logging into the cloud, right, so I’m curious what version’s serial number you’re trying to enter, CS6, or maybe there is some licensing model I’m not aware of?
There is a trouble-shooting document for when Cloud apps are asking for a serial number unexpectedly, which seems to mostly be about the demographic details listed for your profile have things that the licensing process doesn’t like:
http://helpx.adobe.com/creative-cloud/kb/ccm-prompt-serial-number.html