I dialed my Amiga 3000 into the university network (14400kbit, static IP), which of course was connected to the internet. I had previously found
http://elfquest.com/ with the HP-workstations on the campus running Mosaic. I guess I looked at some more of it, downloaded some LaTeX stuff and read some Usenet artices.
Oh, and I had some BBS experience years before, but I understood the question as concerning a TCP/IP, SLIP or PPP internet connection and none of the local BBSs offered this.