Though you opened the HD case and apparently didn't notice damage, it maybe there, just not readily "visible". Since, you done all that can be done on your own, its a "hard error". It maybe even be electronics related as the speed isn't ramped-up and it can't recover data as it should either to a physical error or electronics holding it back. The noise maybe from a bad bearing and nothing to do with the insides. In these cases, a spot of oil on bearing "if" exposed and inverted for
oil to migrate overnight does work. As this is a 20gb size HD, suggests its pretty old and time to pitch it regardless. The problem is not only recovering data, but any spare parts maybe nil. The service is doing abit more to recover, IMHO and cost is justified. Since the system doesn't see the HD, then you've done all you can as any s/w needs a semi-working HD to attempt data recovery. You can google for other HD recovery services from other vendors and see if cost is less.

tada -----Willy Happy