What you need to do is:
1) Unlock the 120gb hard drive with XboxHDM. This is usually done with the EEPROM/key that the hard drive is currently locked to, but as I mentioned earlier, you might be able to use one of the master passwords and save yourself the hassle of needing to use your EEPROM reader.
2) Lock the 120gb hard drive to the new Xbox's EEPROM with XboxHDM. This is basically the last step of whatever XboxHDM guide you might be following. You won't need to do all the other stuff like populating the hard drive.
These are two separate things that might not necessarily be mentioned in the same guide, but you should be able to find plenty of guides and videos for each thing separately. As far as using your EEPROM reader goes, from what I understand, you only need to be able to power the motherboard, so I think that as long as your Xbox can turn on (even if it's not turning on correctly), the EEPROM reader should work without needing to apply external power.