Can't see both monitors

Hello,
I have a Dell dimension 8300 series desktop with a 128 MB DDR ATI RADEON 9800 Pro. The base has a general monitor input, as well as a DVI input. My goal is use my new Samsung 46 in LCD TV, which has 4 to HDMI inputs, as a monitor. I purchased a cable with a DVI on one end, and a HDMI on the other. However, when I connected the DVI cable (from PC DVI input) to the TV HDMI input, my PC monitor stopped functioning ( screen went blank, dark), but the TV worked rather well as a monitor. My question: How can I have both PC monitor and TV, working as monitor, on at the same time?
Thanks for the assistance.