Before the internet was a big thing, what sort of tasks did you use your computer for?
Do you mean the "web", and do you mean NOT Amiga? Really.
The internet pre-dates the Amiga by a *long* shot. And before "your computer" there were terminals, yes, "on" the "internet" since the 1970's. I used to play Star Trek on IBM mainframe terminals on the Plato network in the early '70's, but they were not my computer.
Soon after I booted the shiny new A1000 into WB1.1, I was connected to the real live bona-fide INTERNET! Luckily, the serial ports worked even in OS1.1, and I had some kind of digital interface to plug into, and POW, I was on the honest-to-deity internet. Net News, Mail, the whole shebang. Anybody who ran WB1.1 remembers when that was, and that the WWW did not happen until 1992-1993. The first web browser I ran was Lynx, we had A4000's by then, and I was showing cloneheads running MSWindblows 3.11 the wonder of the Web on an A4000!
So as far as Amigas are concerned, the internet has always been a big thing, especially for developers; MITS and Altair owners, your mileage may vary.