Funny you should ask. Back in January, I wrote a piece on this very subject. Here is the relevant portion of that piece:
I recently came across the question, "Is The Universe a proper noun or not?" The person who answered said that it is capitalized as a proper noun when referring to "our universe" but the word "universe" has a number of meanings. This also comes up with the Bible and the Internet.
Now, the Bible is easier to answer because it's the title of an actual book, but it's also a common noun as a general word for a reference that is considered the authority on a given subject. The word internet is also a common noun that's been used long before computer systems were invented. Most people consider it a proper noun based on the fact that there is only one such system. I don't. It's a personal opinion. Whether they exist or not, private independent communication systems could and may exist that are not or should not be connected to the public internet. When people refer to The Internet, they mean the public internet. (note that I didn't capitalize the word)
Why is "internet" a proper noun?