How can I create a new iCloud account

If you create/use a new Apple ID, you will lose access to some of your data and the purchases made with your existing Apple ID.

Device or computer? What happens when you try to download an app from the App Store? Error message(s)? Account disabled?

See the Apple Support article(s) below. 

Apps won’t downloaded. 

App Store, iTunes Store, or other Apple services - If you can't connect      

If your account is disabled, contact iTunes Support for assistance. See the Apple Support articles below for contact information.   

iTunes Support – world wide 

Apple Support schedule phone call     

Billings and Subscriptions 

If necessary, try Twitter

https://twitter.com/AppleSupport.         

If you still want a new Apple ID, create a new ID (if necessary) and sign into iCloud using the same Apple ID on another Apple device/computer. You should then be able to sign in.

The maximum number of free accounts have been activated

Apple ID - create a new.      

Apple ID – Create        

Apple ID - Could Not Create or Could Not Set Up iCloud message.    

Or contact Apple ID Support.  See the Apple Support articles below for contact information.  

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.   (Link doesn’t always load)  

Get Support          Work through the screens to get a chat option. You may have to pick a slightly different problem.

Apple Support schedule phone call

https://twitter.com/AppleSupport