Personally, I'd say it's
technically correct to capitalize it, because "internet" is a generic term that can refer to any system of interconnected computer networks, but "Internet" is the proper name given to the largest and most popular such system of interconnected networks.
But at the same time, I totally get why it's often left with the lowercase i in casual use, and I do so a lot myself.
I tend to consider it in the same category as a lot of grammar rules that are broken in all but the most formal contexts. For example, one would generally refer to "the New York Times reporter" rather than "the The New York Times reporter", even though "The" is part of the Newspaper's proper name.
Comments
Anyway, I don't normally capitalize "internet".
When I'm referring to a network of connected computers, I say "network" or "computer network".
Of course, this use is all but obsolete these days, since "internet" almost always refers to the Internet.
"thou neededst to know that"?