LG RS232 Commands partially working
First - The manual specifies a carriage-return following each command:


  
  [Command 1] : First command to control the TV.
  
  
  (j, k, m or x)
  
  
  [Command 2] : Second command to control the TV.
  [Set ID] : You can adjust the set ID to choose
  
  
  desired monitor ID number in option
  
  menu. Adjustment range is 1 ~ 99.
  
  When selecting Set ID ‘0’, every connect-
  ed set is controlled.
  
  Set ID is indicated as decimal (1~99) on
  
  menu and as Hexa decimal (0x0~0x63)
  
  on transmission/receiving protocol.
  
  
  [DATA] : To transmit command data.
  
  
  Transmit ‘FF’ data to read status of com-
  mand.
  
  
  [Cr] : Carriage Return
  
  
  ASCII code ‘0x0D’
  
  
  [ ] : ASCII code ‘space (0x20)’
  


The Serial.println function ends the line with a carriage-return (0x0D) and a line-feed (0x0A). Try using Serial.print instead, and manually supply the line ends. The LF is garbage to the instrument, and is likely invalidating subsequent commands.

I would recommend using a computer and a serial terminal while debugging this. You want to make sure you understand the communications instruction set well, before trying to write your own program. If it were me, I would start with a computer and TeraTerm, or something similar.

Second -  Is your cable crossover? Make sure your cable has the correct pinout for a crossover.

Third - Set ID 0 is a catch-all, but since you only have a single display connected to your serial port, it may be more logical to specifically target your ID. This way, query commands will be properly addressed. Go into your TV's Option menu and assign an ID (it probably defaults to 1, which would be fine).

Fourth - Since the Set ID field is a hex representation, it may be expecting a set field width of 2. Try sending 00 instead of 0 - or better yet (per the suggestion above), 01 or whatever your Set ID is.

Eg: Power On: ka 01 01[CR] and Power Off: ka 01 00[CR]

Fifth - Make sure to read the ACK replies to everything.
For instance, if you send ka 01 01[CR], the TV will reply with a 01 OK01x on success.

To query the Power Status, you would send a read request, like so:
ka 01 ff[CR], to which the TV should reply exactly as above a 01 OK01x to indicate that the TV with ID  01 is ON.


Code Listing




Power ON                    : ka 01 01[CR]
Power OFF                   : ka 01 00[CR]
Energy Saving - OFF         : jq 01 00[CR]
Energy Saving - Minimum     : jq 01 01[CR]
Energy Saving - Medium      : jq 01 02[CR]
Energy Saving - Maximum     : jq 01 03[CR]
Energy Saving - Auto        : jq 01 04[CR]
Energy Saving - Screen Off  : jq 01 05[CR] 
Input Select  - DTV Antenna : xb 01 00[CR]
Input Select  - DTV Cable   : xb 01 01[CR]
Input Select  - Analog Ant. : xb 01 10[CR]
Input Select  - AV or AV1   : xb 01 20[CR]
Input Select  - AV2         : xb 01 21[CR]
Input Select  - Component1  : xb 01 40[CR] 
Input Select  - Component2  : xb 01 41[CR]
Input Select  - RGB-PC      : xb 01 60[CR]
Input Select  - HDMI1       : xb 01 90[CR]
Input Select  - HDMI2       : xb 01 91[CR]
Input Select  - HDMI3       : xb 01 92[CR]
Input Select  - HDMI4       : xb 01 93[CR]
Aspect Ratio - 4:3          : kc 01 01[CR] 
Aspect Ratio - 16:9         : kc 01 02[CR]
Aspect Ratio - Zoom         : kc 01 04[CR]
Aspect Ratio - Set by Prog  : kc 01 06[CR]
Aspect Ratio - Just Scan    : kc 01 09[CR]
Aspect Ratio - Cinema Zoom1 : kc 01 10[CR]
Screen Mute - OFF           : kd 01 00[CR]
Screen Mute - ON            : kd 01 01[CR]
Video Out Mute on           : kd 01 10[CR]
Volume - Mute ON            : ke 01 00[CR]
Volume - Mute OFF           : ke 01 01[CR]
Volume - Relative UP        : mc 01 02[CR]
Volume - Relative DOWN      : mc 01 03[CR]
Volume Control [00-64 Hex]  : kf 01 00[CR]
Picture - Contrast  [Adjust 00 - 64 Hex]    : kg 01 00[CR]
Picture - Brightness [Adjust 00 - 64 Hex]   : kh 01 00[CR]
Picture - Color  [Adjust 00 - 64 Hex]       : ki 01 00[CR]
Picture - Contrast [Adjust 00 - 64 Hex]             : kk 01 00[CR]
Picture - Color Temperature  [Adjust 00 - 64 Hex]   : xu 01 00[CR]
OSD (On Screen Display) - OFF                       : kl 01 00[CR]
OSD (On Screen Display) - ON                        : kl 01 01[CR]
Remote Control Lock - OFF                           : km 01 01[CR]
Remote Control Lock - ON                            : km 01 00[CR]
Audio - Treble Adjust  [Adjust 00 - 64 Hex]         : kr 01 00[CR]
Audio - Bass Adjust  [Adjust 00 - 64 Hex]           : ks 01 00[CR]
Audio - Balance Adjust [Adjust 00 - 64 Hex]         : kt 01 00[CR]