I'm trying to work out what is wrong with this laptop. There is a hissing sound coming from the power board mid left. The laptop screen remains off and there is no output to external VGA unless it requires BIOS settings, manual doesn't specify key combination to switch. The hissing sound is also present when either inverter board or lamp is disconnected. The laptop flashes all leds and FDD comes in as it would be POSTting.
It sounds a bit like "coil whine", i.e. high frequency vibrations in a transformer or coil caused by fluctuation in the magnetic field they maintain.
That in itself does not necessarily indicate a failure, but sometimes you can hear this type of sound from switchers straining to maintain the desired output voltage, maybe due to some component failing shorted.
Without knowing specifics of this model, the display may need elevated voltages and there could be a boost converter hard at work.
This does not explain the missing external video output except if something is shorted and dragging down the supply in general. Did you check voltages?
Retrograde's suggestion is most likely the cause... On the video it looks like the sound comes from LCD so my bet its the high voltage supply in the link of yous its called
BACKLIGHT POWER INVERTER MODULE:
There are many possible reasons for this like:
failing caps (electrolytes) of switching power supply / inverter
I see two on the image the black tall cylinders with aluminium top check if they are not slightly lose (can be turn by +/-5 deg radially without bending the pins) or the top is not flat anymore (if it is spherically convex) then it means the cap is bad and need to be replaced.
disconnected load (backlight)
sometimes the connector can get lose and disconnect
short circuited load (backlight)
I saw once (also on laptop) that the high voltage cables where isolated just by tape which in time unstack and the cables short circuited them self after twisting.
faulty backlight lamp
My bet its one of the first two reasons. These converters are usually located on one of the edges of the LCD so try to verify its the case... From the images it looks like its the right vertical edge of your LCD so check if the sound comes from that area: