I chatted with a Linksys support person and they said that the WRT400N doesn't have any facility for enabling IPv6.
If I were to use an alternate firmware on the router, would IPv6 become available or does IPv6 need special hardware?
No ipv6 does not require special hardware, if you installed DD-WRT on your router you have ipv6 options http://www.dd-wrt.com/wiki/index.php/IPv6