Switch it around to get rid of the N/A:
=IF(A1="","",LOOKUP(A1,PARTNUM,PRICE))
Or maybe to cover both zero and blank in A1:
=IF(OR(A1="",A1=0),"",LOOKUP(A1,PARTNUM,PRICE))

I can't tell what you want for the 2 logical questions, though. In
your description I think you left out some AND or OR statements that
would explain better. I think you mean something like this. Which
LOOKUP goes to which?

- IF A1 is not blank, and Sheet2!B2 is not "No", do xxx.
- IF A1 is not blank, and Sheet2!B2 is "No", do yyy.