Ok, so I fixed it though I have no idea what the problem actually was. I tried once more to unplug and reconnect all the hardware, when I remembered the fans in my hard drive cooler were seized last time I spring-cleaned my system. I know a stalled motor draws a LOT more current than a working one, so I disconnected it and everything worked. I cleaned the fans and got them running and put the cooler back in, but on a separate power cable to the hard drive - one that only has fans on it. I installed the second RAM module, but the problem returned so I assumed my power supply just fell short of the systems requirements. I disconnected a USB card-reader and now everything works fine. Oh, and there was also an intermittent problem with the SATA connection on my hard drives board which confused the whole matter and made diagnosis much more difficult.
So...by elimination and trial-and-error, I got there in the end. I have no idea if any of my reasoning was correct, or if I got lucky. But I'm still chalking this one up in the win column.