A drive that spins up but clicks when you try to access it is usually already damaged beyond any reasonable repair. Your best bet, if there is any hope at all, is to try an aggressive back-up program (one that doesn't give up so easily when it sees I/O errors) to try and read any data you can off the drive and copy it somewhere else.
Now, if the drive doesn't even spin, then you may try one of the suggestions above. I've found that slapping the drive usually gives enough of a jolt to break the heads free from the platters and allows the drive to spin up. Be sure the drive isn't spinning already, though, since this otherwise can cause more damage.
I would never open a drive up unless you never intend to use it for data storage again.
The best case for hard drive repair is when there's an issue with the external circuit board. If this is physically damaged or shorted out, you can typically swap out the circuit board with that from an identical model. Once I had 2 identical drives that were broken in complementary ways: one had the click of death (but a good circuit board), and the other had a dead circuit board (but a good mechanism). Swapping the circuit boards yielded one good drive and one extremely dead drive.