Yes, you hold the menu button down for 10 seconds. When the padlock goes from locked to open, release the button.
I had one that got soda spilled into the little PC board with the button switches, and it ended up in the locked state once the board was cleaned. So, I had to unlock it.
Someone left the monitor and a bashed up Dell computer on the end of their drive with a note; "please take - free" - I just knew the monitor would come in handy.
The one I'd been using was scrounged on a free recycling group, they told me it was faulty and the buttons were dodgy, like something had been spilled down the front.
After cleaning the button PCB, I reflowed all the solder joints in the hope the heat would desiccate any lingering residues. It seemed OK for a while, but soon became apparent that the buttons had a life of their own in humid weather.
It got to be such a PITA that the Dell got put into service.
The Dell monitor I had this problem with had 4 buttons. The power button was fine, the other 3 had trouble at different times. They have a small surface-mount capacitor on the back across each button switch. The switches appeared to be well-sealed, but the soda stuff gut under the caps, ate some of the PC board, and caused lingering conduction. So, I removed all the caps, severely scrubbed the PC board with solvent and a toothbrush, and soldered on, I think, 1000 pF caps where the bad ones were. This has solved the problem.
Your results sound EXACTLY like what mine was doing, and I had to remove the caps, clean and replace with new caps. Most likely, it would work fine without the caps. (I have quite a big stash of SMT parts as I assemble PC boards.)
If the switches are not sealed, then they are almost certainly full of sticky, conductive gunk, and would have to be replaced.
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