Holy heck! I fixed it! A fresh flash didn't work (stuck on Samsung logo) so I had to do this
1) Went to http://www.samfirmware.com/
and made an account (it's required if you want to download firmware) [Version: Android 4.0.4
2) Downloaded the oldest firmware available (apparently, "Country: Cellular south" means US)
3) Installed custom recovery in Odin's download mode
(Power+Volume Down). I used the latest TWRP
and flashed an ODIN version of it. Note (heh): Don't use auto-reboot as you need to manually boot into recovery (Power+Volume Up) so that it doesn't default to stock recovery after you flashed a custom one
4) Boot into custom recovery and Advanced wipe everything (which means everything except your internal and external SD cards)
5) Now, set it back into ODIN downloader (Power+Volume down)
6) Use Odin to flash the Android 4.0.4 version you downloaded.
7) Wait a fairly significant amount of time for it to finish.
8) Booted up beautifully and
recognized the S-Pen.