When mine crapped out, I simply took the drive out, changed the jumper to slave, unplugged the ribbon cable & power cord from the new computers CD drive & plugged that into the now slave hard drive.
Then you can explore that drive & retrieve any info you want & click & drag it to the new C: drive
Be sure to unplug the power cord from the computer before opening up the case.
If I can do it with my limited computer knowledge, anyone can.
That is the easiest and safest approach.. additionally, I leave a second harddrive on my PC as a redundant storage center for the important files. Cheap protection.