Apple ID locked. Can’t purchase storage to back up to cloud

Welcome to the Apple Community.

You may need to reset the password(s) to regain access

See this Apple support article, and give it a try, if you wish:

What to do: If your Apple ID is locked or disabled - Apple Support

If needed:

If you forgot your Apple ID password – Apple Support

Eg: says: 

“Reset your Apple ID password on a web browser

If you don't have a trusted device, you can reset your password on a web browser — but the process may take a little longer.

When possible, the web browser will redirect you to a trusted device. If you'll have access to one of your trusted devices soon, it may be faster and easier to reset your password then”.

Reset your password at iforgot.apple.com

All the best :-)