Connect a PS2 to an LCD panel...

I have 2 PS2s and wanted to case mod one. I have an old netbook shell. Therefore I want to try making a PS2 laptop. (I may need to make a new bottom half of the netbook, as the standard one is not deep enough to fit both the motherboard and the disk drive.)

I'll worry about power later, I don't care if I need to use a outlet to play. But now I'm trying to work out the video.

I need to split the signal from the PS2 to rear outputs as well as to an LCD controller board, which then goes to the LCD.

So I thought I'd get a PS component cable http://www.ebay.com.au/itm/Componen...ole-AV-PS-3-/141743420175?hash=item210090f30f
split it, and then connect this to a component to DVI adpater. http://www.ebay.com.au/itm/DVI-I-24...erter-Black-/141772530972?hash=item21024d251c
then connect that straight to the LCD board.
http://www.ebay.com/itm/VGA-DVI-LCD...ch-1024x600-/111741291989?hash=item1a044ccdd5
the other end of the split cable will go to jacks on the case.

Obviously I'll trim the wires to length. It all should be digital, so no converters should be needed, and the PS2 does output YCbCr (digital) according to the settings menu. I just want to know if there are any problems with this video connection that I haven't seen.

(Audio will be worked out later)

It's a slim PS2
Dell Inspiron mini 10v laptop shell
LG LP101WSA (TL A1) 10.1" WSVGA LCD