It sounds as if you're locked in a power struggle. I've been there with other issues, and I've found that the easiest way out is to completely re-envision the conflict. We're unschoolers, and we honestly don't have power struggles over media. That said, we don't have a house full of all the latest gadgets, 500 TV channels, etc. We have a family laptop, which is currently out of order (searching for a replacement), and a kind of standard cable TV package. At one point, our oldest was asking for a Wii, and we simply explained that we felt there were better uses for our money, though if he was interested in earning the money himself, we'd be happy to provide him with a way to do that. He dropped the subject, and seems completely content to play with his cousin's Wii once a month when we're over there.
We also have tons of fun learning activities that don't resemble traditional school work, and that much of the time seem way more fun than watching TV. Honestly, though, I need to be very available to my kids for decent chunks of time during the day. They enjoy my company, and if they had to read alone, they just might choose TV instead. Snuggling up and reading with me, however--or playing board games while eating popcorn--usually trumps the TV option. TV would probably win out over boring workbooks, though, which is why I'm glad there really are other ways to learn arithmetic, for example. My four-year-old is learning basic addition facts from playing Shut the Box, with absolutely no coercion from me. Plus, he's learning the underlying concepts (e.g., that two and two make four, and three and one also make four).
I personally am uncomfortable with a house full of rules; I'd rather set things up to minimize struggle. If the only sweets in the house are a box of fig newtons, and the three kids eat the box at one sitting, I'm not too freaked out because a). they have some redeeming nutritional value; b). once the box is gone, they'll have to select healthier food until the next grocery-buying trip. If I couldn't resolve the media conflict any other way, I'd be inclined to eliminate ALL screens in the house (including mine) so everyone just had access to them during library trips, etc. For me, that would be way better than battling constantly.