I wouldn't use Switch Res - it can cause unpredictable results...

FIRST:
Try connecting to the LED screen directly from the Mac without the TH2G to ensure that you get some kind of picture...

if that works - then:
Try adding a DVA DA (Distribution amplifier) in line between your TH2G and your DVI LCD which works...
if that works ok, then connect your LED screen to the 2nd output of the DA

alternatively - without a DVI DA - program a DVI detective from the LCD screen that works. Then install it in-line (before) the LED screen.

you need to establish whether your mac can output to the LED screen without the TH2G. Once you have proves this - then try the TH2G, then DVI DA, or DVI detective

regards

Simon