This could probably fill an entire separate thread but I love this thought. I am only just now remembering that I actually used to sit down at a computer and .. wait for it.. FINISH. I'd do something.. be done. Then I'd go do something else.
I remember something similar, though the real cause of my time on the computer ending was because I was on dialup and that would tie up the phone line. This was back when I was much younger and with my parents, but after my family moved all of our phones off the landline and to cellular, we ended up getting a lot more use out of the computer. After all, the computer only had entertainment purposes if you had a movie or a game, and all our games were the single player sort. So, with the advent of the Internet, there were things to do on the computer to pass the time, like browse webrings and forums or try and fail to learn Esperanto (and RPG Maker 95, which probably contributed a lot to my interest in game development).
Before all that, I spent a lot of time climbing trees and wanting to be an architect and writer (the latter of which I've been pursuing for a while now). My brother and I'd drag planks into trees and we'd build little things we called forts and make up our own currencies (using the tabs on soda cans, for example), we'd play with our family's chickens and cats, and we'd grouse about picking up fallen apples (because it was boring) and so on. Odd to think how little of any of that I'd get away with now -- now I'd suffer some odd looks from folks for climbing a tree that looked especially climbable. Really, the computer was just for Doom and Encarta and writing book reports. That's just rambling though and not all that interesting or indicative of any change other than growing up a bit.
Unfortunately, I was a child back then, so my memory of pre-Internet computer use is probably different than that of someone who was an adult the entire way through. Would be nice to see a bunch of people writing about it - not so much about how computers and the 'net changed things, but what they were like beforehand without concerning themselves too much with the difference between now and then.
The computer has become infinite. Yikes.