Apple ID and find my

If the only problem is you have a forgotten password, this Apple article has instructions for what to do if you have forgotten your password --> If you forgot your Apple ID password - Apple Support

or go directly to this link --> http://iforgot.apple.com/

If you still need help:

Contact Apple for help with Apple ID account security "This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues." --> Contact Apple for help with Apple ID account security - Apple Support

If you find you can’t sign in, reset your password, or receive verification codes, you can request account recovery (read this support article: How to use account recovery when you can’t reset your Apple ID password - Apple Support ) to regain access to your account. Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity.

When you changed you ID did you actually change it, or did you set up a new account? If the former, your computer should be able to verify and update to any changes you made. If the latter, you will need to log in with the old ID and password. After doing that you will need to get the Mac updated to using your new Apple account.