Even in such a case, if you have set up Time Machine, you can restore and browse the backup data by using another Mac that operates normally. Now let’s see how to restore and view the backup on another Mac.
Prepare
Create the same username on a working Mac as the sick one.
Restore and browse Time Machine backups on another Mac
Open Time Machine in Finder’s Applications folder Right-click on it and select “Browse other Time Machine disks” from the menu that appears. This will bring up a window that says “Select a Time Machine disk to browse”, select the disk you want to use and click “Use Selected Disk”. Then, the restoration screen of Time Machine is displayed like this, so See here for other Time Machine usage and settings.
Mac - How to use and set up Time Machine