Some kind members helped me to get the phone running again and then getting TWRP 188.8.131.52 on it with the 4.1.2 build.
This was flashed to the phone using Odin after using E-Z Unlock 1.2 to unlock the bootloader and install TWRP 184.108.40.206.
I saw some random issues when I would reboot or power off and on with it locking on the Samsung Galaxy S III logo... but the phone rebooted eventually and I was able to continue use.
Fast forward to today -- for the first time in awhile, my battery fully discharged. When I got home, I plugged in and tried to power on my phone. Locked at the Samsung Galaxy S III logo... EVERY. TIME.
So I go into recovery... I find that the first thing that greets me is a message asking me for a password. This is odd, since I never put a password on anything... I try to mount the system/cache/external partitions. I try to factory reset to try a different rom. I'm told it works but there's a failure message because of E: cannot decrypt data. I try to flash a different rom anyway. It says it was successful. I flash the gapps, more success messages. I try to reboot and again I'm locked at the Samsung Galaxy S III logo.
Random side note -- sometimes my Samsung Galaxy S III logo has a blue android cat of some sort on it... not sure where that came from (one of the CMR flashes when I was trying to fix the phone, methinks).
It's so strange -- because I was obviously able to load a custom ROM with the current bootloader and recovery -- and now after my phone's battery drained, I'm back to being dead in the water... I really need to get to the bottom of having my phone boot into a ROM reliably.
Previous ROM was Gummy Nightly 01-06-14.
New flashed ROM is CyanFox 2.0.2.
Please help. I need my phone up and working as soon as possible here, I'm expecting important calls in the morning, so this is horrible timing.