Dear Amanda,
I just ran into the same problem. Did your computer come loaded with other security software, like stuff by Norton or McAfee? Once I uninstalled McAfee from my new computer, uninstalled Avast!, rebooted, reinstalled Avast!, rebooted, and I was able to access the internet.
Also, make sure that Avast! has permission through the firewall. If you're using Windows Firewall with Vista (since you say you've got a new laptop), go to the Control Panel, and under Security, there's an option to "Allow a program through Windows Firewall." If Avast! doesn't show in the program list, you can browse to it and add it.
Good luck!
Nicole