The AC plug seems to be loose inside the monitor.

Hello there:
Normally the electrical connection has a molded piece that holds the part in place and somtimes they will have a piece that slides in a slot that goes around the part and secures it to the frame of the monitor thus allowing for a tight fit.
If you are capable of doing this type of a repair you can unplug the monitor and discharge the power from the monitor by taking a screwdriver and laying it across the two terminals to discharge the capacitors. now you can saftley open the case and look at the part that is in question and if you can replace the part or it just might even be able to slide the piece back in place ok ?
so these are some options for you to try and if not than i would take it to a professional that can repair it for you ok?
I really hope that this has been very helpfull for you.
best regards michael

have it check, or might be better have it replace, any connection regarding electric current supply should be tightly connected, if it is loose, it might cause some serious problem like short circuit or even worse is FIRE, just bring it to the technician and have it change, also with your power switch