Yeah, I've heard that sound. It's usually followed immediately by a "CLUNK" as I toss the disk in the trash.
If the disk shows up in the BIOS disk scan, or when Linux detects the disks, you might still be able to get some data off of it with dd. That'd be my first plan, if I were in your shoes.
If that doesn't work, you might have some luck with the logic assembly replacement idea. If it's the controller circuitry that's out of whack, it might be fixed by a new board. If the motor or head are actually sticking and unable to do their job, it's a more dramatic situation. And, I'm not sure what the mechanics of such things look like these days. This might be one of those situations where putting the platters in another identical drive is the only option.
Did you say "recent backups"? Ha. That's funny.
Yes. You'll learn. Someday. The cost of not learning is infrequent, but can be very, very, high.