Is the ID one of the old ones which isn't an email address? You have to use an email address as an ID to use iCloud. You would need to change the ID, and this involves signing out on all your devices and signing back in with the new ID. This is the procedure you should follow if this is the case:
Firstly, if you have 'Find My iPhone/iPad/iMac' enabled on any of your devices, turn it off.
Create a new email address, for example at Yahoo or Gmail, or anywhere convenient (or you can use an existing address as long as it has never been associated with an Apple ID).
Go to http://appleid.apple.com and click 'Manage your Apple ID'. Sign in with the current ID.
Where it says 'Apple ID and primary email address' and gives your current ID email address, click 'edit'.
Enter your new address and click 'Save changes'.
Now you will need to go to each of your devices and sign out in System Preferences (or Settings)>iCloud - 'Sign out' on a Mac, 'Delete this account' on an iOS device (this will not delete the account from the server).
Then sign back in with your new ID. Your iCloud data will disappear from your devices when you sign out, but reappear when you sign back in.
I re-iterate: before you start, turn off 'Find My Mac' (or whatever) or you will need the services of Support.
If your ID actually is an email address then there is a less obvious problem and you may need to contact Support.
