hi floppy,
i can confirm, the establishing of your modem-connection looks pretty good.
but your dns points in the wrong destination...
check your resolv.conf, it points probably to your local router for your lan-connection.
so better delete your /etc/resolv.conf that your ppp0-session can create a new one,
that is appropriate for your modem-connection.
you need the right dns-routing for your modem-communication...
and on the other side check that your lan-device is down,
f.e. with "sudo ifconfig eth0 down".
good luck, you've almost succeeded!