Count # of rows that meet a criteria

Hi there!

Excel Spreadsheet example can be downloaded here.

I need to have a single cell giving me the total number of rows that meet the following criteria:
1. Row does not contain an "X" in Columns B:F
2. Row does not contain a number that is <=0 in Columns B:F
3. Row contains at least one number that >0 in Columns B:F

In this example the answer would be 2 (Rows 4 and 8).

Making Column G use a formula for each row and then doing a sum at the bottom is not an option. It needs to be a single cell. Any ideas? Thanks very much for your help. I've been puzzling over this for a while now.

~kory