You can purchase a new EEPROM. When you do this, you do not purchase the EEPROM chip itself, but the key on it. There is some risk to purchasing an EEPROM, because you do not have any defined guarantee that the seller will not sell it to other people or will not use it himself. You're best of purchasing from people you trust and from people with good references.
Once you have the EEPROM data, you can use ConfigMagic to write it to the EEPROM in your motherboard. This will effectively remove the ban on your Xbox, and you can then connect to Live with the same account. This time, make sure your mod is OFF!!! Many people recommend customizing your BIOS so you know if it's the retail or hacked BIOS - colormods, fastani, no ani...whatever.