I retrieved the hard drive earlier today. Not good news, unfortunately.
The whole casing still smelled from the explosion that took place therein. I didn't see a mark on anything at first, though, and tried not to disturb too many of the contents in case it sent more of the stench around. Opening the case alone did enough of that, after all.
As I went to disconnect the HDD cabling, the connector felt strange - it turns out it was half-dessicated, and it crumbled as I pulled it away from the drive (my hands were coated in this black scorched stuff, and I had to go and wash off the stench of burnt electrical death afterwards; The black stuff came right off, but it took a couple of washes for the overpowering smell to fully go away). After I got the drive out, I saw that a large chunk of the PCB on its underside was scorched. It's not worth the risk of hooking it up, so I'm glad that I had an up-to-date backup. The few files that it was behind by can easily be re-obtained from my other half and some relatives (some photos I didn't yet have on my backup drive), and from Amazon MP3 and Google Play Music (some music files I'd bought), and I already re-grabbed my two Lix levels from here yesterday - I'm really glad I uploaded them when I did, now!
I now understand roughly what must've happened. As I'd suspected, the power supply went loco. It was suggested to me that it may have had dud capacitors within which would have caused this to occur, and I'm guessing that that was indeed the case, because by the looks of it, it sent a massive charge into everything that was connected to it, wrecking the whole lot.
I've decided to stick with docking my laptop into my USB hub (to which is connected my keyboard, trackball, joypad, and now my ex-backup HDD), speakers, and monitor, as I have been doing for the last few evenings, as I'm getting on really well with this. This saves me hassle and money of dealing with another box for my desk, regardless of architecture, and means I only need to get a new backup HDD, now.