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!

have you tried putting FALSE in quotes "FALSE"?

Just fyi, TRUE and FALSE are recognised terms in excel, and can be used without ""