In the 1970s, Indiana University had a plasma screen terminal they called the Plato System. I saw the game Empire being played on that system, a top down graphic image of a federation or klingon ship, and you could go looking for other ships to attack, which were other users located on university campuses scattered over the country. It even had a primitive chat box, where you could post a message and others could see it.
One of the reasons I got hooked on computers and ended up with a degree. So I went to IU, very first class I end up
keypunching, uggghhh. Underclassmen got the crappy equipment, isn't that always the case? We actually had a Texas Instruments computer where you had to flip switches, which represented 'on' or 'off' for each bit in an instruction, then press a button to enter that instruction into it's memory, then flip the bit switches for your next instruction...... all the time I'm thinking, get me to the dang federation, man, come on.
So, I don't know if that was the 'internet' per se, but the idea that you could communicate with multiple people at the same time on your screen from locations around the country, that
still sticks in my mind. This would have been 1977 plus or minus a year.
p.s. - as an unrelated afterthought; One of the crappier projects I worked my way through in those years was creating a Compiler in Assembly language. Puke.
Since someone brought this thread back up, here are a couple of pictures of the Plato terminals.... and that first glorious, multiplayer, networked game from the 1970s: