Not sure about how much power the monitor would draw, but I hooked up a current meter to the AC input of my P3 500 (Katamai) machine. Once it got into windows, it leveled out at ~100Watts (Just under 1A current draw @ ~119VAC). With a TV tuner card in action, I'd expect to tak ~ 20W onto that.
Bottom line...a new TV would be cheap to buy and WAY cheaper to run
EDIT: out of curiousity, I decided to measure. My 21in Monitor pulls ~120W with a browser window with a bright background maximized, ~90W with only dark desktop showing