Bellsouth DSL - working offline?

I have recently gotten Bellsouth DSL over the last month. Everything has been decent. Speeds weren't as advertised at first but last week started blazing at the 1.5Mbps as sold to me. Well another problem started. You can be online looking at stuff, then when you try to go to a new page or back up, a "connect" popup comes up saying I need to connect, and dial-up connect at that. It's like the line is down but all the lights are on steady at the modem. I think this may have started after a ZoneAlarm update but not sure. Any ideas? Is this my pc issue or Bellsouth issue?