Somehow through tweaking pfSense and configuring the Squid package the cache files started to fill. At first I was particularly confused if Captive portal was still on as every site I was trying to get to required a login -- failing to do so kicked me out with an Error 504. The Squid service also refused to be started.
At this point I proceeded to re-install Squid and noticed that even without it the continuous login request persisted. By some luck I started to play around with other pfSense options and checked the disk space -- BAM! Thats where it dawned on me that my Squid cache had absolutely filled my 80GB hard drive and there were but a few KB of space free?!
Now that I knew the most probably reason, that launched a few searches on how to properly clear or compact the cache. pfSenseDocs has a guide. Using the Command option under Diagnostics didn't seem to help as the disk space didn't change. On initial setup of Squid, I had to twiddle with a few settings via terminal access on SSH and this is where I remembered that under System -> Advanced that Secure Shell was on -- and that is what I did.
1. SSH into pfSense will drop you into the same menu you'd see if you had a monitor connected. Choosing option 8 gives you a shell.
2. From there I shut down the Squid service and proceeded to delete everything under /var/squid/cache
3. Once space had been free'd, initiate squid -z to recreate the required directories.
4. Reboot pfSense and,
5. you can now run the Squid service
Problem solved! Now to keep watch on disk space and tweak how much cache info is kept.