An update, I replaced the regulator and it supplied a steady 5v to the display board and to the sensor. I had a look at the display board and couldn't see anything obviously wrong but without a circuit diagram etc. I'm a bit blind (and very out of practice with electronic fault-tracing).
I ended up putting my hand in my pocket for another display (£18). Fitted it this afternoon and it's working fine.
Maybe the display board died and took the regulator out? Anyway, fixed for less than 20 quid.