The first Star Trek episode I saw first run was "Elaan of Troyius" in 1969 (I was six); and I was hooked (I was really into NASA and the Moonshots then too). Caught up with all the rest of the episodes in syndication in the early 1970ies; and I remember getting the Franz Joseph Tech manual and Enterprise Blueprints in 1975 because I had the chicken pox; my sister knew I like Star Trek, saw it at a bookstore and thought it would cheer me up; and take my mind off scratching.
I also got into computers because of Star trek (not in the way you might think). In 1975, I found out my Jr. high school had a teletype hooked into an HP2000 mainframe via 110 baud acoustic modem; and one of the things you could do on it was play a 'Star Trek' simulation - and I was hooked (I was also sad to learn modern computers of that day had no voice interface.
I learned my first programming language (after finding out what the SSTR1 program was written in), because I wanted to take what the original programmer had done, and update and modify it a bit more to my (and others) liking. I spent a year creating my own offshoot of that original program (with a nod to the original author), and everybody liked the updates/changes I'd done and I had incorporated a lot of feedback from those of us playing the game at my school. Little did I know it would lead into the career I have today.