I had a PFS box that with similar(if not exact) problem as what you described, all the settings are okay, webGUI okay, captive portal radius auth okay, even package info display nicely(if internet down it will say sth like can't access server), but just no internet connection on the user side. The issue fixed by reinstalling the squid package. My squid is on transparent mode.
Did you try to reinstall the squid package to see if it can help your issue? Your squid is in transparent mode so it is capturing all port 80 traffic automatically but it is not proxying them out. Did you see anything funny in the squid cache.log? Did your squid use any disk cache? What is your hdd usage?
Or apparently the most direct way backup your settings, factory default your PFS, and restore them back, the squid would reinstall itself and settings will retain(once an internet connection hooked up to WAN), be warned that I never try this on any snort.
Better if you have another spare machine, set it up as PFS, and try on that. So you won't ruin the old PFS further.