http://www.tiaowiki.com/w/Extracting_key%2C_spoofing_firmware_and_flashing_XBOX_360_Lite-on_DVD_drive_using_JungleFlasher_in_Windows_%28No_PC_Freezing%29#Get_the_key.2C_dummy.bin_and_other_files
The full dump is called the
dummy.bin It will include the key/indentify/inquiry/drive serial in 1 file. Here is what I mean in the tutorial -
http://www.tiaowiki.com/wiki/images/0/0e/14.jf.load.JPG
And even if you couldn't get the full dump, you are always able to replace your dummy.bin dump with either stock/ixtreme firmware, inject the key.bin file into it, and then repair the drive serials from the LiteOn barcode/PCB. Manually spoofing will do this quite easily. I have a tutorial here -
http://www.tiaowiki.com/forums/xbox-360-hardware-talk/how-to-spoof-and-flash-to-a-new-liteonbenq/ (see the bottom of thread). This manual method will be the same as getting the full dump.