Sir Kyle Aziz
Caleidah
It'll go back to the good old days, aka the 10k(?) years where the Imperium was closed off from Terra. We'll be plagued from all sides by horrible forces. Some sectors will be annihilated, others will band together to form new areas. If a new Emperor is born, splendid. Woop-dee-doo. He'll be skinned alive by all of the psychopaths out to make him a god.
The only problem I see with that, is that other races will still use the warp, while the Imperium wont be. As it currently stands alot of places will simply starve to death without Agri worlds. The Necrons, Tyranids, Orks, Tau, Eldar and Chaos will still be a problem.
They don't use the Astronomican, so they're not hindered. Unlike when the galaxy was cut off by savage warp storms, no one could really do much by traveling through the warp.
Except, Humanity is basically screwed without a new Emperor, and as Mac said. The Webway gate which the Emperor currently sits on will be opened, and Terra will fall.
You never know. The Web Way Gates would open without the God Emperor being there, but perhaps that would be a good thing for Humanity with the Emperor gone, whatever would pop it's head though the Web Way (More than likely to be an Eldar) would soon be crushed under the might of the Inquisition Terra would still have it's military to beat the day lights out of whatever comes out, and perhaps from their take the webway as their own way to travel. Yet, I guess that depends what is on Terra at the time of the Emperors fall....Not that he ever will! All Hail The Immortal God Emperor!