There seem to be versions of the Abyss kernel for many different devices. Can you post a link to the version you flashed?
But, it probably doesn't matter. Since you're in the Sprint sub-forum, I assume you have a Sprint S3? If so, I'm really sorry to tell you that you've bricked your phone. The Omega ROM, from everything I can see, is for the international version of the S3 (i9300), not the Sprint version. I REALLY wish ROM developers would more clearly describe their products. Different versions of this phone have different cpus and different radios, and therefore different firmware to map to those features. The international ROM you flashed is looking for hardware that doesn't exist in your phone.
I REALLY wish ROM developers would more clearly describe their products, but I also wish people who decide to flash ROMs would do more research first.
Anyway, do a Google search for JTAG and you should be able to find people who can reflash the stock software, for a fee. Several people on this forum have reported good results from this service:
JTAG Unbrick Service - Bricked my Phone
Good luck.