My first computer experience was in high school around 2000-2001 for computer programming in C++. During break times, we would play some games installed on the computer by the teacher. But no internet was there in school as teachers are scared of students accessing X-rated content.
So from friends I heard of "Internet cafes". They would charge you hourly for computer usage. I would make a list of things I want to search during the week. On weekends, I would go to internet cafes and search for these things.
From 2005, I got my first computer in my home with Internet connection.
Videos had to be downloaded to be watched. No streaming. Torrents and P2P software like Shareaza, Limewire were used to download videos of all kinds.
Music streaming I think existed back then. Sites like Raaga, MusicIndiaOnline were streaming music.