Worthless, no, as I do a lot of writing and editing on my computer. Likewise, my music library would not be affected by the lack of internet. Actually, I had a computer for several years in the early 1990s before I had the internet, which only arrived in my home years later, and broadband, later still.
However, I must say that I spend a lot of time online, and not simply on MR, for research, and email, and stuff related to research. Also daily news, both print and video, as I don't watch TV. So, yes, the internet is a necessary and vital part of my daily life, and my computer would be a lot less useful if I didn't have access to it.
Cheers