grammatical number - Is singular or plural standard for state of none of something?

As a rough rule of thumb, I would suggest using the singular if the normal state of affairs is for there to be "either zero or one" of the given item, and the plural if there's no 'expected' number as such.

It would probably be more common here to use the plural, because we don't have a sense that "a room normally has one ball in it". A room isn't specifically designed for holding balls, and the number of expected balls in a room isn't "zero or one".

However, the singular is much more likely in a case such as:

There's no car in the garage.

because we have a notion that 'a garage usually fits one car in it'.

(On the other hand, if your particular garage happens to be a very large/shared one, then the plural would then be appropriate.)