Well...we have a daughter who loves tv and a son who loves the computer. We were concerned with the amount of time they were spending and the amount of unhealthy media exposure they were getting. We had battles when we tried to get them off as well. We decided to run an "experiment". Since my husband and I grew up running around outside after school we wanted to see if we could encourage our kids to do the same. We stopped our cable so we got no channels and cut our internet service at home as well as purged all video games out of the house...we gave ourselves a 1 month trial...the first 2 weeks were rough. After this, we noticed the kids find other, healthier activities such as biking, swinging, going for nature hikes, playing board games, and even reading!! We have lived without a tv or computer games for the past 4 years and didn't miss it!! We have slowly allowed the tv, internet, and computer games to trickle in at a pace that we are comfortable with, but we notice that the kids don't seem "addicted" and don't give us any trouble when we tell them they have had enought time on it like they did in the past.
I think that we learned that children today see so many adults on phones, computers, and the internet that they just want to do the same and can't control the duration as adults can. By replacing the activities for a period of time, they will slowly want to do other things. Good luck!!