I think I must contribute to the topic, as I have almoust miraculously found out how to fix the issue in my case, and this might help others.
It turns out that in order for the buttons to work, your fingertips have to be at least a bit electroconductive.
All the times that I tried to hold the buttons for 15 seconds in order to unlock the monitor - my fingers were very dry, and I failed. I never knew that dryness was the reason for my failure until by occasion I spat on my index finger in order to scrub some spot from the screen. I scrubbed it and then without much hope tried to hold the buttons, to see whether by any chance this time the monitor will unlock. To my amazement, this time the monitor unlocked.
So, the conclusion holds: keep your fingers conductive when you use capacitive buttons!
Hope this helps =)
To Dell support: you might consider including this case in your KB.