IE is always in offline mode and always asks to conenct via Dial-up

Hello all,
I installed IE7B3. Now it always says me that it's in offline mode
and tries to dial to internet. Of course it fails, because it picks
the modem of my mobile phone which is not turned on. Now, my network
configuration is a bit tricky - I'm conencted through LAN to the
gateway of my internet provider. Also I have second LAN card to share
this conenction with my girlfriend's computer and some VMWare adapters.
I have two dial-up adapters - a VPN to the office and a modem of my
mobile which I don't use actively but keep it because its settings are
very cumbersome to re-create.
Apparently IE always tries the dial-up connections before "seeing" the
LAN connection.
I'm sure that the LAN conenction is OK, because I usually play an online
game and it does not have connectivity problems. Also, Opera happily
browses the web sites I point it to.
A very unfortunate side effect is that my anti-virus application appears
to use the same libraries as IE to conenct to internet and it cannot
update it's signatures (cause it believes i'm offline).
Another problem is that when the AV application tries to update itself,
the "Dial-up Conenction" window steals the focus of the full-screen game
and this usually leads to the death of my character and loss of my team.
It's not fun when it happens every 2 hours.

I checked in Network Conenctions -> Advanced Settings and my LAN connection
is listed first with dial-ups last.
Any solution is welcomed.
Regards,
Todor