No if you lost all the regions on the ROM (Flash Descriptor, ME region, BIOS, GbE), then you are correct you will need a full dump of the entire SPI image from someone else's machine (but you will have to change lots of things, serial number, MAC ID regions, UUID etc). But even if you got that, you will need to disassemble your computer and use a SOCI-8 clip and CH341a programmer to burn the new information back in.
You will need to look for the EEPROM chip. There are probably 2, one for the EC and the other for the BIOS. Alternative is to buy a pre-programmed chip and either solder that yourself or have someone do that for you. The chip will probably be a Winbond and should start with 24 or 25. It will have 8 prongs.
have a look at this http://forum.notebookreview.com/threads/official-alienware-13-r3-owners-lounge.797884/page-890, here someone had a similar problem with theirs after an bios update. Look at the picture to see what the EEPROM chip looks like. Practice dumping the info from these chips. A flash programmer like AsProgrammer_1.4.1 or even flashrom (linux) will be useful to actually read/write to the ROM chip.
I'm still not clear, how much can you actually boot up to now? Does it POST?
If you manage to dump the SPI image, upload it here so I can look at it.