The Runner cannot play Emergency Shutdown if the only successful run against HQ made that turn was made while a Crisium Grid was installed rezzed in the root of HQ, even if the Crisium Grid was trashed during that run.:Ruling
Do restrictions such as those on Emergency Shutdown and Successful Demonstration count as abilities? That is, are those cards affected by Crisium Grid? Restrictions count as part of card effects, so you cannot play those cards if the Runner made a run on a server with Crisium Grid.