The warp storms that cut off Terra and so many others was do to slaanesh's 'birth', think labor/parturition, and then there was one giant warpstorm that resulted in the eye of terror, think birth.
I know we're arguing semantics, but I'd figure the 10,000 years before the Fall would be closer to gestation since Slaanesh was only beginning to "coalesce", per the Eldar codex.
And the birth of Slaanesh did more than create the Eye of Terror, it also wiped out the Warp storms throughout the galaxy, as I said. From the Eldar codex:
"For ten thousand long years before the Fall, the Warp had been riven with storm and tempest, making it almost impossible for the vessels of the lesser races to travel between the stars. With the birth of Slaanesh
, the Warp was becalmed, its rage temporarily spent."
The warp was never "shut" to Terrans, it was just so dangerous to use only madmen and adventurers did it before the Fall.
From the Forgeworld book Horus Heresy: Betrayal
, it says that during Old Night "...Old Earth, or Terras as we know it, was totally cut off from its colonies and allies."
We know that there were some gaps between the Warp Storms because Mars was able to send explorer fleets out to found new Forge Worlds, but apparently the Terrans weren't so lucky.