when you turn the knob to the steam side, can you hear the small clicking noise it usually makes? from the video, it doesn't seem to be clicking as the hot water side does. based on this, and the fault symptoms, it sounds like the steam switch has remained shut when the knob has been returned to neutral.
the machine thinks the steam section is open when the knob is in the neutral position which doesn't allow any water to flow. this would then cause an error as the machine doesn't know what's going on and just doesn't operate.
i'd just remove the top casing and check the steam switch to see what condition it is in, you'll be able to see fairly easily if it's got any problems. it is also simple to remove. if it does have a problem, you can disassemble the switch and clean it up, but if there's visible arc damage or melting near the switch contacts, just replace it.
the BES820 is easy to disassemble and reassemble so there's no real loss from having a go at it.