Count Non-Blank Rows

It effectively counts the number of non-blank (>0) rows in an array. This
formula is limited, however, in that every column requires a separate
statement. I would like to find a function that could handle an array of any
size with a single statement.
100
110
000
001

3=SUM(IF((A1:A4>0)+(B1:B4>0)+(C1:C4),1,0))

1=OR(A1:C1>0) for
every row in the entire array. Unfortunately, according to this document AND
and OR functions cannot be nested within SUM+IF statements:

Dim oRow As Range
Dim cNonBlanks As Long

For Each oRow In Range("50:80").Rows
If Application.CountA(oRow) <> 0 Then
cNonBlanks = cNonBlanks + 1
End If
Next oRow