Why would 2 toolbar apps in XP suddenly stop recognizing my internet connection?

These programs, Weather Watcher and Gmail Notifier, have successfully run on my computer for several years. All at once, both of them are saying there’s no recognized internet connection, even though I have broadband and am connected.

My firewall is set to allow full access to both programs. I tried various tweaks and nothing is working, including uninstalling/reinstalling. Anyone have an idea?