In your frustration you are forgetting one important thing: You control the remote. Don't allow the TV to be turned on except at specified hours for programs of which you approve.
I am sure you read the recent recommendations of the American Academy of Pediatrics: Children younger than 2 should not watch any television. I think that is a wise recommendation, and I would stick with it. If she cries or has a tantrum, simply put her in her room and shut the door until she stops. If she asks for the TV, a tape or a CD when you read to her, simply tell her that you won't compete with the distraction, and put the book down. Then try again later. And make a bargain with her. If she listens attentively while you read the book, she may watch TV for 30 minutes.
Television is a wonderful addition to our lives, but it can become a tyrant. My guess is that your daughter's constant demands for TV represent a control battle as much as a true preference. As much as possible we want to avoid these battles. But in this one, it is important for you to win.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.