Restore Backup from another Computer

Always include exact PC model and version of Windows in your posts.

Do you just want to copy personal files over to new PC?  What software did you use to make the backup and where is it saved?

Does that software allow you to "mount" its saved backup file as a drive with its own drive letter?  That would let you open, copy, delete any file in the backup like it's an ordinary file so you can copy to the new PC.

If old PC is still working, you could install Macrium Reflect (free) and use it to image the drive with the files you want to recover. Save that image on an external USB drive.

Then install Macrium on the new PC and mount that image file saved on the USB HDD as a drive and copy your personal files onto the new PC. Don't copy any Windows or app files.

Hi

I would say YES.

Lenovo Migration Assistant for mine, so the DELL equivalent.

OR the HDD/SSD maker website maybe.

Worst case scenario 

https://www.microsoft.com/en-gb/windows/transfer-your-data