I think the inventor did want to apply for patents, but he was advised not to. Or something like this, I should pay more attention in class...
Its a poly-archy. Everyone running a server or a cable on the telphone line, or a hosted piece of intellectual content owns the medium of the internet. But the internet it self is just a concept; the inventors at CERN might claim ownership but annonymous user adaptation has changed it so much from the origional intellectual property that I doubt a court, at least in scotland, would rule in their favour. So in a sense everyone participating in the internet owns it; while at the same time no one does.
I don't know who's in control of the main servers that provide services for lower tier services (wow, I think I actually learned something!), I'll try and find the sheets in which it explained stuff about it and see if it says there. So, I'm guessing the Tier 1 ISP's are the ones "in control" of the internet, but apparently, there's no formal list of who is in Tier 1. There was kind of a cool quote that said "If you wonder whether you're Tier 1 or not, you're not".
Everyone with a networked computer owns part of the internet. No one could be said to own it entirely, and even large ISPs don't actually own anything but the physical apparatuses that enable 'official' internet connections.
Keep dreamin, communist dogs! Wouldn't you all be too busy trying to farm and mine coal to go on crraaazzzyy space shit like the internet anyway?
Those good for nothings at Google are the most popular indexers of the internet so in a sense they own it. If something is not on the first page of their index it might as well not be on the internet.