First off, ignore the manual regarding power.  There is no way to power up
these sets via the serial port because it is connected to a CPU that is
powered down.  Only the MICOM can reset the CPU and get it going again.

After obtaining a schematic from jenya on lg-hack.info I have to
revise the above.  There is some hope.  The RX pin is shown as
optionally jumped to a pin marked ISP_TXD which carries the following
note: "Interrupt for ISP wake up in STB Mode"

Just sending the documented power up sequence doesn't do it but perhaps
some other attention signal might snap it out of a deep sleep.
Will try sending long breaks, etc.  And even if I don't succeed you
might since it is marked OPT.
 
Pin 4/DTR on the serial port is wired to a pin marked
IR.  After a careful look it appears to indeed be an output.  Can't
imagine a good use for that but there it is.  The pin looks like it
should have +5 on it if the IR pin is low and drop low if the IR
pin goes high enough to switch on the transistor.  Somebody at LG 
wanted to be able to hook up to the serial port and get access to the
raw infrared signal.  Something that would be behind the set and
thus unable to have its own IR sensor.  Perhaps a LodgeNet box?  So
there is a good chance there is a secret knock to enable some
features like putting up arbitrary OSD info and such.

Beyond the commands documented in the official manual, the serial
port has additional commands.

Taken from a service manual for a 32LG2100
aa 00 00 [Enter Adjust Mode]
xb 00 40 [Component1 Input (480i)]
ad 00 10 [Adjust 480i Comp1]
xb 00 60 [RGB Input (1024*768)]
ad 00 10 [Adjust 1024*768 RGB]
aa 00 90 End Adjust mode

 RS-232C COMMAND
[CMD ID DATA]
Wb   00 00 White Balance Start
Wb   00 ff White Balance End 

        Cool   Mid   Warm
R-Gain   jg    Ja    jd
G-Gain   jh    Jb    je
B-Gain   ji    Jc    jf

Edid data and Model option download (Engrish in original)

Item			CMD1	CMD2	Data0	Description
Download 'Mode-In	A	A	0 0	When transfer the 'Mode In'.
						Carry the command
Download		A	E	00 10	Automatically Download
						(The use of an internal pattern)


Per user uzivatel on lg-hack.info the following is a shortcut to the
tool options

Read out with:
tool options1: ab 0 ff
tool options2: ac 0 ff
tool options3: af 0 ff
tool options4: ag 0 ff

Set with a wierd syntax where a 16bit value gets broken up

Example:
Send: af 0 0df a80
Recv: f 00 OKdfa8x
This puts 0xdfa8 into tool option 3.

He has also worked the exact bits on some of the Tool Options.  He
never says for sure what model he is basing this on but one example
implies 37LH7000

Tool Option 1
Bits	Function
12-15	Inch 0100=32, 0101=37, others may be:
		0000=19, 0001=22, 0010=26, 0011=27, 0110=42, 0111=46,
		1000=47, 1001=50, 1010=52, 1011=55, 1100=60, 1101=70
10-11	Unknown
06-09	Tool 1101=90, 1010=70, 1001=60, 1000=50, others may be:
		1100=85, 1011=80, 0110=45, 1010=41,
		0100=35, 0011=30, 0010=20
03-05	Maker 011=LGD 10bit, 100=CMO (CHI-MEI), 101=AUO (Acer) 8bit, 110=Sharp
00-02	Revision 0-7

My set has thirty four options for Tool so at least bit 10 is now
dedicated to that field.  My choices are different but bear some
relation to these..  All of the proposed sizes seem to check out on my
set.

Tool Option 3
Bits	Function
15	0=no EMF, 1=EMF
13-14	00=No Divx, 01=Divx SD, 10=Divx HD
12	Bluetooth 0=off, 1=on
11	Digital Eye 0=off, 1=on
10	Headphone 0=off, 1=on
09	OPC 0=off, 1=on
08	EPA 0=off, 1=on
07	e-Manual 0=off, 1=on
04-06	Audio Amp 000=NTP3000, 010=NTP3100, 100=TAS5707, 110=STA339
02-03	LED Type 00=Normal, 01=Moving, 10=Moving Sound
01	New E-Con 0=Off, 1=On
00	Reserved