Hi nick england,
Welcome to Adobe Forum,
Creative cloud do not need a serial number. it will be using your aadobe ID on which you have purchased the creative cloud membership.
So you need to login with your Adobe ID and password to activate the cloud membership.
In case it is not signing in successfully please try the following:
I dont know which operating system you are working on so i am giving you some steps windows and MAC OS:
In windows 7 navigate to following location:
1. look out for "Hosts" file
2. Open it with notepad
3. Check if you have any entry for Adobe
4. Remove the entries and try again launching any product from CC
1. Please click on "Go" and navigate to /private/etc
2. Open "hosts" file and check out for any entries for Adobe.com
3. Remove the entries and save the file
4. try again launching any product from CC