the PC never turns off power to the monitor, it has its own power.
and sure, the monitors all do that 2004 to now. called VISA sleep.
modem has nothing to do with this.
Some monitors have this features called that.
its in your users manual. 2009m?
your page.
https://support.hp.com/us-en/product/hp-value-20-inch-displays/7274733/model/3884700/manuals
the words are clear.
it has power saver mode, turn that off
it has osd LOCK,
but no powerlock. as some do,. as your manual. shows.
page 24 shows.
http://h10032.www1.hp.com/ctg/Manual/c01725831
quote, power button does this.
turns the monitor on and to standby or sleep mode.NOTE:
The power button is located on the top or front of the monitor depending on the model
off , on, and sleep.
my guess you are putting the power button i Sleep mode
a feature of this monitor.
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