Moving files from a Broken iMac

Solution 1:

You may be able to use a disk recovery utility like Disk Drill.

Recovery utilities scan the blocks on the disk and attempt to string the blocks together into whole files. I don't know how well they work with HDDs taking from a Fusion drive, but you have nothing to lose.

Downloading Disk Drill (and similar software) is free to install and scan your disk. But you will need to pay if you want to recover any of the files it finds.

Solution 2:

Yes you can, as long as you put the disc in a usb 3 enclosure, compatible with your new Mac.

Edit after result of diskutil cs list.

Your HDD is part of a Fusion Drive :

HDD present :

+-< Physical Volume FF551275-7077-4759-870E-2AA51B847383 
                ---------------------------------------------------- 
                    Index: 1 
                    Disk: disk3s2 
                    Status: Checking 
                    Size: 999345012736 B (999.3 GB) –

SSD absent :

+-< Physical Volume 5CA40245-A547-42CE-A283-8A855191C7F5 
                | ---------------------------------------------------- 
                | (No properties) –