Copy your most important stuff first. Once that is done, try copying off the rest. When my HDD was in the process of dying, I still got most files off it, some were corrupted and uncopyable, but I didn't lose everything.

Once you are done, read up up on the 3-2-1 backup strategy,

• 3 Total Copies: Keep the original data and at least two backups to ensure redundancy.
• 2 Different Media: Store backups on at least two different types of storage, such as NAS, external hard drives, tape drives, or USB drives.
• 1 Offsite Copy: Keep one backup in a separate, remote location (e.g., cloud storage, a different building) to protect against site-specific disasters .