dropped my external hard drive -- buzzing noise and beeping follows.

keep on trying to get it to run. turn it on and, wait, and off again over and over again. you never know, i recently saved about 75% of a friend's data off a failed/failing hard drive which at first sight wouldn't mount. i just kept on power cycling it and all of a sudden it mounted. it was possible to copy data to another drive, just not very much at a time before it crapped out again. i repeated this procedure until it wouldn't mount anymore even after dozens of power cycles.

anyways, your case is likely different from that but i'd give it a shot.

as for affordable data recovery, it doesn't exist. if you're real brave you can get yourself another one of the exact same hard drive model and try moving the platters from the old one to the new one (in as dustfree an environment as possible). never tried this myself, also there's often differences in build even withing the same model.

as always, it's a matter of how important the lost data is.