from my experience, it is likely a capacitor dying, most often one of the power supply bulk cap will do those noises before outright dying, if you have soldering experience it is an easy and cheap fix (look for a bulged or leaking cap, replace with one of similar capacity rating and superior or equal voltage and temperature rating).
one other thing if you dropped it pretty hard could be one of the ferrite core in the high voltage inverter (assuming pre-LED backlight era panel) then as long as it still work and is not dropped again it will continue working, although a bit less efficiently than before.
there can be other things but i fixed about 5 monitors with those exact symptoms by changing a bulk cap often harvested from dead PC power supplies, and once seen a broken ferrite core do those noises but i do not even remember in what it was.
and there kinda is liquid in an LCD, all the electrolytic capacitors do contain liquid electrolyte (not the kind you drink
) and as far as i know liquid crystals are true to their name, although pretty thick and in very small quantity.
and to your last question, dying caps can blow up or burn, but in almost all the screens i fixed all of the circuitry is in a steel shell and on all the pcb i ever tried to fix i only ever seen one blown (although it was from a lighting damaged power supply, it was not fixable in the end) and one burned (on an old compaq motherboard, only half of it burned before failing open and did not do more damage than a bit of suit on the drive cages), so it is not dangerous inside, and completely inert if unpowered.
