Can the non-working computer ping the router ahead of it?
I have no router, but switch with 16 ports instead.
Yes, from 2nd host I can ping ipv6.google.com, I can ping :2 - remote gw of he.net, and I can ping 1st host ipv6 addresses, and vice versa - when I ping three v6 addresses on 2nd host from 1st host the pings passing ok.
Moreover, I did tests with IRC server connections, and this is what I received:
>irc *635 -h 2001:470:28:*::123 efnet.portlane.se
*** Connecting to port 6667 of server efnet.portlane.se
*** Couldn't bind to IRCHOST[ Whois *635!*@tunnel*-pt.tunnel.tserv24.sto1.ipv6.he.net (Network) ]
-- I tried to connect with this ::123 host to efnet.portlane.se (v6 compatible server), but I get "Couldn't bind to IRCHOST" and then I get connection with default :2 host as you see, which is resolved.
Another test with standard telnet:
>telnet -b 2001:470:28:*::90 efnet.portlane.se 6667
Trying 2a00:1a28:1100:7::1337...
Connected to efnet.portlane.se.
Escape character is '^]'.
NOTICE AUTH :*** Processing connection to efnet.portlane.se
NOTICE AUTH :*** Looking up your hostname...
NOTICE AUTH :*** Checking Ident
NOTICE AUTH :*** Couldn't look up your hostname
NOTICE AUTH :*** Got Ident response
-- as you can notice - the connection passes ok, even irc server drop me notice about unresolved host which is :90 one.
At first I thought it was ircII (irc client) problem - but I compiled newest version and got the same "Couldn't bind to IRCHOST".
Any ideas?

I still wonder - why 1st host have this "ip6tnl0" in ip list while 2nd host does not...