Okay. You can try one of two things.
The simple and hopefull wishful thinking one is defragment your HDD, and hope it's a corrupted file that the 360 will catch. Turn on your Xbox and connect to XBL. From there go to the "My Xbox" tab and move all the way to the right, "System Settings". Inside there, with your HDD connected, go to "Memory". You should see where it says "Hard Drive", or whatever you code named your HDD. DO NOT click this. Instead, while "Hard Drive" is highlighted, press Y on your controller. You should now see "Rename" and "Format". DO NOT click these either. Highlight EITHER of them and press "X X LB RB X X". It will ask to perform maintenance. Say yes, and it will be done in a few seconds. Hopefully this fixes it, along with freeing up a few KB of memory on your drive.
If that ALSO does not work, you can try the two step process. Start up POL, and open your disk tray without logging out. Then go back into POL to see the gray "YOU LOGGED OFF WRONG STUPID!" screen. Reinstall from there. This will erase any screenshots and macros you have! Make sure you send the SS' you want to keep to your email, and save your macros to the server. Refer to wiki to learn how to do this.
If FFXI *STILLLLLL* doesn't want to work, go back to the gray dummy screen and UNINSTALL everything. This will nerf all files pertaining to POL and most of FFXI. Now...install again. And if you have the WotG disk/vana collection '08/'09, I HIGHLYYYYYY suggest you also use those, because 360 has severe lag downloading files way more often than not, and a *** of updates have happened in the two years it's been on 360. Leave it updating overnight and see if you can log on in the morning. Goooood luck.