EDIT: Solved the whole RADS Error problem. I can launch LoL now, but it says my server status is undefined and play button is greyed out. And no, thereisnourf level doesn't fix my problem..
This means that something on your local network or connection is completely cutting you off from LoL.
Most often this is a firewall or antivirus program. If that's not it for you, you'll need to figure out what else on your connection is causing the issue.