multiple criteria count

In my problem I have 2 columns(a2:a351 and b2:b351), each containing data, however some cells are empty. I want to be able to count when each corresponding set of data(ie, a33 and b33) are both non empty cells. So if the entire data was to be all blank, the count should be 0 and if each cell had data in it the count would be 350. Data is on sheet 1, columns b and c. Count is on sheet 2, column c.

This is the syntax that was recommended to me: line (c2, sheet2)
=SUMPRODUCT(--Sheet1!C2:C351<>"")--(Sheet1!D2:D351<>"")

I have been trying to use the count and sum functions in numerous different ways but have had no luck whatsoever. Here are some of the syntax I have been trying.

=COUNT(IF(A2:A351<>"0",IF(b2:b351<>"0")))
=SUM(IF(A2:A351<>"",IF(B2:B351<>"",1,0),0))
=COUNTIF(A2:B351,AND(A2:351<>"",B2:B351<>""))

I think the SUMPRODUCT was the correct approach, the format appears to be wrong. Try this:

=SUMPRODUCT(--(Sheet1!B2:B351<>""),--(Sheet1!C2:C351<>""))