I don't have the original eeprom either, I took a backup of the eeprom on a fully working v1.3, used liveinfo to load and edit the eeprom to change the serial number to be the same as the shagged xbox, (eepromagic tells you what serial number it wants, you can also check the serial number on the sticker on the bottom of the xbox) then flashed the shagged xbox eeprom.
Some steps which might help you do this:
Make sure you have the latest xbtool, v1.0.22, or it won't work.
Go here for the xbtool documentation:
http://home.alltel.n.../XBtoolDoc.htmlXBtool, load your bios, eg. 4981, and choose the '1024k' option at the bottom of the screen.
Copy your eeprom.bin file into the xbtool\patchdata folder, then choose the 'embed eeprom' checkbox.
When you click 'save as', it will save the bios as a 1024k bios with an embedded eeprom. Flash your modchip with this bios.
Install flashed modchip into the shagged xbox, and boot.
Copy the eeprom.bin file we spoke about before onto the c:\ of your xbox.
Copy the eepromagic app onto your xbox.
Load eepromagic and flash the eeprom.
I hope I've got the correct sequence of events here, I don't want to mislead people, however if your xbox eeprom is already corrupt, you can't make it any worse. I've just recently carried out this procedure and I now have a working xbox again.
Triggernum5 and Evil Ryu state you don't need to have matching serial numbers, I prefer to, I also don't want two xboxes having the same serial number.
Hope this helps.