Also, I don't want to say that they are horrible parents, because they are doing what is right for me. Even if I don't like it, I have to deal with it. If I did say that, then I'd most likely get my computer and video games taken away for a long time.
They are not doing a good job as parents. At age 11 I didn't spend much time on the computer. When I got my laptop, they allow me to be on the internet all I want. I have similar issues like you, because my laptop is now too old to comfortably play Minecraft. So I play on the family iMac that barely gets used otherwise. Really, my mom has an ipad she's always on, and my dad has multiple laptops. So I'm really the only one who uses it. Anyway, they're really brown town about me using it for some reason...I have my own account on the computer, and it's the FAMILY iMac, not to mention that if they aren't using it, me using it actually is making use of the 1200 bucks they shelled out on the thing. Plus if my mom wants to use it while I'm playing I just get off...keeps her not mad...so it's less of an issue now but I digress...
For your case, I'd imagine you'd have to have done some crazy stuff to have your parents not trust you at that age. All you can do is work your hardest to either repair the internet capabilities on your computer (can be a number of issues, hurr) or you can earn their trust back. Not knowing what you did, I can't give any advice there. However, you need to explain to them EVERY time you use the computer, exactly what you're going to do. Parents will always assume the worst, so when you say "didn't want to bother her" she sees it as you taking an opportunity to sneak on.
Let's say you want to use the computer to check your email and update a game. Tell them: "Hey mom, since neither you or dad are using the computer right now, I'm just checking with you to make sure it's alright if I check my email and update a game on steam. I'll be off in 20 minutes, and you can watch me do this if you really don't trust me like you said."