I appear to have fixed the problem.

I carried out the following steps - I don't know if they are all required or only the last few, but this is what I did:

• Disconnected the monitor from the PC, so there was only a power cable attached
• Unplugged the monitor from the power source
• Holding down the Power button (R) on the front of the monitor, I plugged it into the power source (initially started colour screens) and continued to hold the Power button until the screen turned off
• I then reconnected the monitor to the PC and powered up the PC, letting it run for a few minutes until I judged the login screen would be available
• I then turned on the screen, using the Power button (R), (which now worked) and logged onto the PC
• I started running Chrome and then tried pressing the Menu button (L) on the screen - it now worked too and a menu appeared
• Using the minus (down) key on the screen (2nd L) I moved down and selected "Factory Reset"
• Pressed Enter and the Menu button again (to clear the menu from the screen)
• At the end of my session I logged out and shut down the PC as normal - this time the screen went to black instead of cycling colours.

When I turned on the power today, the screen remained black until I turned on the PC and the normal startup screens began - so it appears to have been fixed.