Hi MEMJC,
SInce you can connect to secured wireless networks, this is very unlikely to be a Norton firewall issue. Norton will detect when you are on an unsecured network and will automatically set a Network Trust Level of "Protected." All that means is that communication from other devices on the same network will be subject to the same firewall rules that are applied to traffic from the internet - so changing the trust level should not disrupt your internet connectivity at all.
Use the Firewall Reset option in the Smart Firewall Advanced Settings to reset the firewall to its default configuration. This will make sure that no custom rule is inadvertently causing the issue. This really sounds like a networking problem, rather than a Norton problem, so I would try some of the networking troubleshooting utilities in WIndows before going to the trouble of uninstalling and reinstalling Norton. Even if it is Norton, it is likely to be a misconfigured setting rather than something that is broken that would require a reinstallation at this point.
Your best option is probably to research some articles online concerning connecting to public wifi to make sure that all of your WIndows network settings are correct. You are right that you really need to troubleshoot this while it is happening.