I have an old broken viewsonic VG150 LCD monitor. Basically, it cannot be
turned on even though the adapter is supplying a healthy 12V DC (measured
with load).

I opened the case and measured a pin labeled +12V and found only 2V when
the power switch is held down, and goes to 0V when released.

Forget what I said about 2V. I measured the wrong pin.

Surprisingly viewsonic gave me the repair manual, but I have to sign a NDA.
So I can't reveal too much here.

There is an IC that implement the power switch toggle effect. That is where
the problem lies. The front panel power switch is connected to the clock
input of this flip flop via some RC network but for some reason it doesn't
want to flip. If I manually connect the +12V to the set or reset pin of this
flip flop, I can turn the monitor on / off at will. So I can add a toggle
switch to do this; it would just look a little ugly.

I hope other LCD manufacturers are as nice as viewsonic in providing circuit
diagram. Has anyone ever obtained repair manual for other brand of LCD
monitors?