C-Cloud stores the backup settings and the machine information in your (%appdata%\C-Cloud). When you move to a new machine, these information will not be available there.
So now, when you download and install C-Cloud on your machine, and sign in to your account, if you have already reached the maximum number of computers*, you will be asked to delete or archive the older machines in order to be able to add the new machine.
The good news is that C-Cloud has a De-Duplication feature that will prevent uploading the same previously backed up files again. For more information, please refer to this article.
* C-Cloud Home users can back up 1 machine only but C-Cloud Business users can back-up up to 3 machines\user.