So we gave up and enjoyed checking out everyone else's geeky stuff, and it was great, and we went home, and we plugged everything back in the way it was in the morning, and it booted and ran fine first time.
So, I conclude, that the explanation is one of the following:
1. Our board likes using analog composite video out, which is what we have here, a bit more (but not enough to be deterministic even here) than digital HDMI-to-DVI-D which is what we had in Exeter; or
2. Our board likes the power supply in our house better than it likes the power supply in Exeter Library; or
3. Our board doesn't like being too close to sea level; or
4. Our board likes the east Somerset bit of the earth's magnetic field and doesn't like the Exeter bit; or
5. Our board, with no sensors attached, likes the angle of incidence of sunlight here and doesn't like it further south and west; or
6. Cosmic rays mumble mumble; or
7. Kinda y'know quantum <waves hands>.