I'm not allowed to get a PSP unless my parents can disable the internet, and preferably if there is a password for my parents to use. Is there a parental control panel with internet restrictions? And if not, is there another way to permanently block internet access?
While you cannot disable Internet connectivity as a whole, you can disable the Internet browser using parental controls.
You'll need to go to Settings > Security Settings, set a parental controls password (0000 being the default), then enable Internet Browser Start Control.
Source: Playstation Knowledge Center
Wanted to make comment can't sorry
They could also use OpenDNS to shield all devices in you home as it will handle filtering for them.