I first programmed a computer at university in 1966 (like, really before the Internet, or even ARPAnet*, was invented) as part of my Engineering Science degree.  But there's an older member here who is a computer geek - he could have started before then.
* mind you, ARPAnet was being designed at that time, and reached initial implementation in 1969.
Yes, although my first real programming was done in 1973, which was the first time I was close to a computer I could get to.  It was a Honeywell H600 (later I moved on to a Honeywell H6000).  I had gotten interested in computers in 1964, but they were all hidden behind locked doors.  I did write a heck of a lot of code in various languages over the years (
Languages).  And most of it written on teletype machine keyboards.
And moving on to DEC PDP machines, Vaxen, and others.  I actually didn't get a person computer until 1992, since I had such powerful machines at my disposal at work.  
Good times, those.
Ah, yes, acoustic modems,dot-matrix printers, punch cards, FORTRAN, BASIC, COBOL, I remember these.