I have a syncmaster 2433bw (DVI) connected to my samsung 40" (using HDMI to DVI dongle) in dual monitors. I have had no problem with getting both displays being displayed at the same time.
What is the max resolution supported on your LCD TV and 2033 respectively?
I am using a 3870 which has 2 DVI outputs running on Cat 9.12. Try:
1. disconnecting then reconnecting each monitor in turn whilst booted
2. check that both monitors are recognized in both windows and in CCC (they should be in "duplicate" mode). if your LCD TV displays desktop upon boot, "swap" displays in windows or CCC
3. make sure your syncmaster 2033 driver is installed. the LCD TV should show up as generic pnp monitor in device manager
4. it could also be a refresh rate/resolution issue. to check, in CCC>desktop properties, under HDTV, desktop area should be selected as 1920x1080 and refresh rate should be set at 60Hz. if max supported resolutions are not the same change the res to match the HIGHEST res possible on both (ex if your 2033 supports 1920x1080 and your LCD TV supports 1680x1050 try changing your 2033 res to 1680x1050)
PS im a NOOB so im not at all technical. more like, fiddle around until it works.