When parents stop their kids using the internet it's usually because they are afraid of something. Nagging your parents wont take away their fear. It won't stop them wanting to know everything that u r doing online, either.
If u r being stopped from using the internet, there is only one way u r gonna change an adults mind: u have to sit with them and show them how U can use the web safely. Try these out:
Show them this site and explain tell them what the main messages are (even if they don't get it, they'll be more comfortable if they know that u do)
Show them that scams and spam safety applies to every age group of the dangers
Sign a Contract that u r both happy sticking to. Take a look at a sample contract and then add or delete your own rules
Remember, adults have seen those news stories of people being raped, abducted, bullied and harassed. They think that it could happen to u and that scares them. Fear has lots of expressions, and people have different ways of letting it out.