I have (2) Asus 27" monitors and (1) Hisence 42" LED TV screen.
Is it possible to have all three connected to an AMD Radeon HD 6700 video card on my computer as one whole desktop?
Your graphics card would need more than one VGA/HDMI/older connector to do multi-monitors. This is what a VGA cable looks like:
This is what an HDMI cable connector looks like:
Once you've got the monitors both connected with either a VGA + HDMI or VGA + VGA or HDMI + HDMI (all demanding on what slots your graphics card has) you can right click on your desktop, and select "Screen Resolution" on windows 7. On XP you go into display and look for "Screen Resolution" or something like that. From the resolution window, you can set up displays on 'extend' mode (which is having two desktops) or 'duplicate' (it...duplicates the two displays)
Just look on the back of your case for the connectors.