Our best hope would be exploit devs, cryptographers and infosec professionals with reverse engineering skills. It's incredible what some people can do with a black box system and no tools aside from a voltmeter and logic analyzer. First you probe the chip with the voltimeter to find where data is being interchanged, then you hit it with a logic analyzer to look for patterns, then you start breaking it down with cryptanalysis, which is really about finding patterns in noise. I think you'd be surprised what the best minds would be able to decipher, given the right hardware and unencrypted data. If the data's encrypted, it gets a lot harder, especially if the encryption is advanced enough that it basically looks like noise. But even then, there has to be some bootstrapping process, so we'd be able to reverse engineer that part of it, and then would need to hope to find an exploit in the encryption.
Regarding cables and such, you'd have to expect that you wouldn't just find a single isolated hard drive. Even if you didn't have a full system, surely there would be cables and auxiliary components strewn about. And if there weren't, their absence would probably be significant, since you'd know they used some material that didn't survive as long as the material used to make the hard drive, and could infer its properties from that. So you'd probably be able to piece together which cables plugged into which components and make educated guesses about voltages and the like.