Question : formula for different conditions

I want a formula that does the following:

If E* says Yes and if VLookup(D*,'Parts'!A:A,1,false) bring backs a value, then i want it to say yes

If E* says No, and the date in F* is prior to august 3rd, and the same vlookup returns a value, then i want it to say yes.

If the vlookup returns no value then i want it to say no and if F* is august 3rd or later, i want it to say

Any help is appreciated

-Brandon

Answer : formula for different conditions

Here is the file, after fixing the worksheet name and reapplying my formula.