Just double-check all the cables.
Plug it into connectors that you *know* work. There's a small yet significant chance that the SATA or molex connector's screwed.

Failing that, open the case, and put your ear to it. If it's not spinning up properly (you'll hear it repeatedly 'click'), try waiting for it to cool down, starting it up on it's side, or hitting it gently as it spins up (these have all worked for me at some point).

The freezer trick above is well known to work as well, but I've also heard that the drive becomes truly shafted after doing it, so it's really a last resort.

The logic board can definitely be swapped out quite easily, but 99% of the time it's either the main motor or the head that's gone, so success is usually unlikely.

Failing that, you can for a price take it to a data recovery service, who'll strip the whole thing down and move the platters onto a working drive.

EDIT: As you can tell from bobzarkoff's comment above, I made up that 99% figure. Give it a shot.
(rpozz, Thu 1 Oct 2009, 0:36, 1 reply)

Aww
You reminded me of my first ever PC (I was about 10, and it was cobbled together with a few of my dad's spares).

The HDD was about 20MB, MFM standard (where you had to issue the 'park' command in DOS before turning it off if you didn't want to risk wrecking the drive). I had to rest it so that it stuck out of the 5.25" slots slightly so that I could bounce it on the case to convince the motor to spin. Fun times :) I even had to pull the lid off once and kick-start the platter spinning with my finger... I don't know how but somehow it continued to work contrary to the usual wisdom that as soon as you get a speck of dust in the head will hit it and cause all sorts of hell.
(Cloudane, Thu 1 Oct 2009, 0:46, closed)

I have a machine here with a 5MB hard drive.
Just about works, but sometimes makes a nasty noise.
( idonthaveafunnynickname Drink-Aware? Sure. I'm aware I want another drink., Thu 1 Oct 2009, 3:32, closed)