OK I should clarify everything:
softmods all exploit a bug (what one does not really matter, more here:
http://www.se7ensins.com/forums/xbox-softm...-explained.html ) that allows them to patch/replace the BIOS with a nice homebrew capable one (in software which first has to be loaded, hence the inability to bypass everything/change some of the first things to load (background colours of the logo) like you can with a chip/TSOP flash and the need for a lockable HDD).
Various softmod methods also have two safety features called shadow C and virtual EEPROM (I got that the wrong way around above). They are usually the "recommended" route for any graphical installer softmod and indeed I highly suggest using them.
Shadow C takes some drive space but in doing so it means you can not overwrite the drive in a meaningful way (some games like to try and update things and it negates most of the risk from messing around with things).
virtual EEPROM is a similar idea but for the EEPROM in the xbox, this EEPROM holds things that makes your xbox yours including keys vital for the xbox to work (
http://wiki-scene.com/EEPROM_(Xbox) ), a virtual one exists that allows things to happen but protects your original. It is however not the same as your original and dumping it is a pointless activity.
Thus to do some of the more elaborate mods involving hard drives you have to bypass these safety features.
In your situation: I would try it first, I agree it may well be the file you want but some installers (like AID) insist on backing it up again when you install a new dash (I assume you changed from the one the initial softmod gave you) and as this is likely after you initially installed the softmod this new backup may well be the virtual EEPROM.
To test, easiest way is to grab your supposed dump and a program called liveinfo (I assume you are familiar with auto xbins if you have a 360 flashing session coming up). If not it is an app that allows you download files MS might not like all that much from a semi-private FTP server called xbins that hosts just about everything xbox and xbox 360 related.
http://360mods.net/index.php?name=Download...tails&id=29
"/XBOX/PC Based Applications/eeprom tools/liveinfo/" is what you want (go with beta 3).
It should spit out a serial number which you can then match to your xbox.
Some guides you may find useful:
http://wiki-scene.com/EEPROM_(Xbox)