I already have 2 screens on my PC. 24" (1920x1080) and 22" (1680x1050). I wanted to connect my PC to TV. I bought a DVI splitter and connected it on the 24" DVI port.
connect PC -> TV : working
connect PC -> monitor : working
connect PC -> DVI splitter -> TV and monitor : NOT
I don't know what's the problem, but I noticed that when I use the splitter my PC don't do anything, it's like when nothing is plugged :(
This is what my splitter looks like : http://www.computercableinc.com/ccinc/images/Splitter-Cable-DVI-D-MF-HDMI-F-Startech.jpg
2) ( Leave TV Unplugged from splitter)
3) Ensure PC Powered off
4) Plug Splitter into the FIRST port of the FIRST video card. Some machines have issues with multiple displays on single ports.
5) Plug Monitor 2 into port 2 / video card 2 of pc
6) Turn pc on.
You should at this point still be able to use both monitors.
If it doesn't work, power down, and switch the splitter and monitor 2 cables from your pc.
Once you get both monitors working with the splitter, plug the hdmi cable into the splitter from your tv in and turn the tv on. Ensure that the tv is tuned to use the hdmi 1 or whicher hdmi input you use. This may sound patronizing, but ensure that you are using HDMI INPUT X from your tv, as this is the cable sending data into your television.
It seems like you have tried most of this already, but keep these points in mind and you may very well get it all working.
If the above doesnt work, and you can get any monitor working when you go through the splitter, you may have a bad splitter. Note that using the splitter will not give you 3 monitors, but will mirror monitor 1 (the monitor sharing the port).