how to log in to existing account on another macbook

Hi nellie181,

Welcome to the Apple Community, where some of us do our best to help each other.

Sorry your MacBook is broken.

Wondering if you backed up your files in iCloud, or an external hard-drive, or anywhere else ?

If so, you may be able to access them from another Mac ok.

Else:

Seems you may need to set-up sharing on your Mac if it is not too badly broken to do that.

If you can:

Apple Support has articles online to help you:

Share your Mac screen, files and services with other users on your network

https://support.apple.com/en-au/guide/mac-help/mchlp1125/10.15/mac/10.15

OR

Allow the App "Apple Remote Desktop" to access your Mac

https://support.apple.com/en-au/guide/mac-help/mh11851/10.15/mac/10.15

OR

How to share the screen of another Mac

https://support.apple.com/en-au/guide/mac-help/mh14066/10.15/mac/10.15

It may be that your Mac is so broken that you are unable to access it at all.

Learn more about what’s covered under your warranty,

costs for repair outside of warranty, and more for your specific Apple product

https://support.apple.com/repair-products

OR

There is a "Get Support" link to Apple at the top right of this discussion page.

OR

Contact Apple for support and service:

See a list of Apple phone numbers around the world

https://support.apple.com/en-us/HT201232

If your country is not listed: 

Apple Assistance:

Choose your country or region:

https://support.apple.com/choose-country-region

Hope something here is of some help to you :)