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PCMCIA Ethernet would be by far the best solution (although good luck on the drivers) if you can find someone who has a dusty old card sitting around on a shelf somewhere, preferably with the still hopefully good driver floppy. Look for cards that don't have the bumps on the top of the connector.
Meanwhile Sony was following up their tremendous success on the PS1 with what was hyped up to be a technological tour-de-force with the PS2. Third party developers couldn't wait to sign up and sell a million copies of whatever they put out.
The final nail in the coffin is that SEGA's first party development teams were just kind of bad at their jobs. A problem that exists even today. Sonic titles are just a solid stream of garbage since the end of the Genesis days. Nintendo has a similar problem with third party support on their consoles, but it doesn't matter too much because they put out a handful of really excellent first party titles each year to keep the platform alive. If SEGA had been putting out a killer Sonic game every year they probably could have kept the Dreamcast going and maybe made some headway against the PS2, although the PS2 was such a juggernaut that it would have still had an uphill battle.