The way I interpret the question (and I could be wrong!) is if all of the precedent cells are empty then to 'not display a result', whilst if any of the cells contain a number then a result should be displayed (including 0 if that is a result).

To do that I'd use a formula (or variation thereof) like this:
Although, to be honest, the empty string causes problems if further arithmetic is performed from it. In my worksheets, I'd keep it simple and just display the 0 all of the time.

My 2c...