Ah, you beat me to it!
As NAT says, I pretty much followed the link's advice (no recover discs or any external props).
I had to use ALT-F10 to get a menu to come up though, and after it scanned the HD it decided I had no option but to restore settings. Fortunately I'd backed up my data (and more importantly, photos) very recently.
There's probably some computer-based lessons for me to learn here, but I'm just glad the thing turns on again now
Thanks to all for advice and moral support, making me feel a bit less rubbish-with-technology.