Later in its life, the Dreamcast release the "broadband adapter", a 100mbit Ethernet replacement for the modem. Worked great, but very limited support in games. That plus a DC keyboard and mouse made me BRUTAL in quake 3... until someone worked out how to join DC games from the PC.
I actually had to go check to make sure the DC did originally have a modem before posting. I've been dabbling in Dreamcast modding the last couple of years, and the only network adapter that came to mind was the broadband one which, colored my childhood memories a bit. I remember there being a very specific reason we couldn't get the DC online, and "not having a long enough ethernet cable" definitely wasn't it.