Trouble with nested if/and statements

Hello! Hopefully my problem has an easy solution. I have an If statement that tests for multiple conditions, and it either always returns true, or alwasy returns false. I think this is because I'm not listing my conditions in the right order.

The setup: I have 3 columns involved in the formula, and a box on another sheet controlled by a checkbox.
The columns are Cert?, Cert #, and Price. The check box is for whether or not a cert is needed (since not everything has a cert #).

The formula goes in the Cert? column

My conditions:
If the Price column (Z3) is blank, then blank
If the Price column is not blank, then test the checkbox ("Sheet2"$B$3):
If the checkbox is FALSE, then "Ok" (because I will use all selections if a cert is not needed)
If the checkbox is TRUE, then test the Cert # column (W3)
If the Cert # column is blank, then blank
If the Cert # column has a number, then "Ok" (because if a cert is needed, I am only interested in the selections that have a cert #).

I have tried the following formulas with no luck:

=IF(Z3="","",IF('Sheet2'!$B$3=FALSE,"Ok",IF(W3>0,"ok",FALSE)))

=IF(Z3="","",IF(AND('Sheet2'!$B$3="Ok",W3>0),"Ok",IF('Sheet2'!$B$3=FALSE,"Ok",FALSE)))

Any help would be very much appreciated!