Concur. If there’s truly an imminent hard drive failure, GET THAT DATA OFF!
You can always scan it on another machine, and you can always delete the copied data if we’re wrong about failure and nothing’s infected, but it sounds to me like your OS install was ruined when the hard drive began to fail. Seen it before, got damn lucky that it was only the OS eaten. Managed to save every relevant file including game saves from the user directory, and stuff on the desktop.
But, use it as little as possible in the process of simply getting the data off the drive, and prioritize. The less that’s done to the drive, the more chance you’ll be able to save more/everything before complete failure.