Following this post : Performance tip for Ubuntu Edgy and Feisty users (via Digg !), I discovered some info on ubuntuforums about the /etc/hosts file.
My internet access problems always falled back on the same symptoms: if at startup I had no IPv6 line in the peripheral tab (I refer to System>Administration>Network Tools>peripherals tab> show eth1 in the network peripherals drop down-list), there was no way I could access to the Internet (NOT an hardware issue – I use a xDSL triple-play provider, TV, VoIP phone & Internet access through my wife’s i-book are always OK). When (after a reboot or two, or three, or four… waiting an hour, or two, or three…) I had the IPv6 line, all was OK.
When I say no way, that was no way. Neither sudo ifdown eth1 && sudo ifup eth1, nor sudo /etc/init.d/networking restart could do anything (beleive me I tried). Nada.

So I peered at /etc/hosts and commented all IPv6 lines as such :
127.0.0.1 localhost.localdomain localhost myhostname
127.0.1.1 myhostname
# The following lines are desirable for IPv6 capable hosts
# ::1 ip6-localhost ip6-loopback
# fe00::0 ip6-localnet
# ff00::0 ip6-mcastprefix
# ff02::1 ip6-allnodes
# ff02::2 ip6-allrouters
# ff02::3 ip6-allhosts

Since then, no more problems. I mean IPv6 shows in the right tab anytime, and I can access Internet…

[Edit] LEETturtle teaches how to remove IPv6, for Internet speed reasons.