I'm 25 and I was around computers since I was 8 or so, but haven't got one of my own until I was 13. However, I skipped the dial-up stuff and got broadband fairly recently, some 7 or 8 years ago.
That said, I obviously remember my pre-internet life well enough. And how was it? Well, great, actually! My neighbourhood was full of kids of my age and I was out a lot, which, I guess, wouldn't have been the case if I had internet access that early. Later, as a teenager, I had some difficulties obtaining new music. I had to find someone who had the specific album and record it on a blank casette. Yeah, you heard it, a CASETTE. Google it! It was tedious, but it had a certain charm to it. You appreciate the music more if you have to go through a bit of a struggle to get it.
Gamingwise, getting a new game was a nuisance for obvious reasons, and PC and gaming magazines were the source of news and info on new games. Solving a game puzzle was more interesting, sometimes frustrating, but helluva lot more rewarding without walkthroughs. And just sitting in front of computer screen felt more isolated and secluded.
So, I guess it was quite different, and many a thing is way easier nowadays, but guess what. I wouldn't have it any other way. I mean, today I'd probably become clinically psychotic without the internet, but I'm glad I was born before it.