I'll help you out.
What happens when you get banned from live is: Live bans that particualr xbox serial number/onlline key/MAC address. All of which are stored on the EEProm. The EEProm is a little chip on the mobo, its sole purpose is to contain the ID information for that particular xbox.
To get back on Live all you need to do is: Download configmagic 1.6 either from avalaunch, or the usual places. Then go to the B/S/T buy an unbanned EEProm for w/e version xbox you have.
To reflash your EEProm you need to: FTP into the xbox, go to the folder with configmagic in it. Open it, and then open the DATA folder. In the DATA folder there is a file named EEPROM.bin, delete it. Then take the unbanned EEProm you just bought and change the name to eeprom.bin, then FTP it to the DATA folder. Once you have that done, get on your xbox and open up configmagic. Press start to bring up the menu, choose unlock HDD. Once your HDD is unlocked you can proceed and reflash your EEProm. Copy down your video region and dvd region, they need to be the same on the new EEProm, if you live in america it should be NCST and 1. Now press start, and select load EEProm from BIN file. Once it is loaded make sure that the regions are the same as the banned one, if not choose change EEProm on the fly option. Once the regions are the same, press start and select update EEProm. It will create a back up, then flash the EEProm.
If it was a good EEProm your back on Live.