Conditional Formatting: Distinguish between zeros and blanks

I have four columns of numbers.

Sometimes the numbers are > 0. . . sometimes they are all zeros. . . and sometimes they are blanks.

I want the conditional formatting of any one row to pick up on when all four cells have zeros, but ignore when they're blanks.

Any suggestions? When I use sum(A1:D1)=0 it also returns a true value for blanks.

Maybe AND(SUM(A1:D1)=0, NOT(ISBLANK(A1:D1))) ?

To best describe or illustrate your problem you would be better off attaching a dummy workbook. The workbook should contain the same structure and some dummy data of the same type as the type you have in your real workbook - so, if a cell contains numbers & letters in this format abc-123 then that should be reflected in the dummy workbook.

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There is a COUNTBLANK function.