Vlookup Combined with If/And Formula

Hi

I am struggling to return a specific result when using a vlookup which needs to be combined with an If/And formula. Also, there might be multiple potential results but with all, some, none matching. Example is below:

Col A Col B Col C Col D
Product Code Sale Start Date Sale End Date
apple AB2 03/02/2016 03/02/2016
orange AB3 03/02/2016 03/02/2016
pear CD1 03/02/2016 03/02/2016
orange CD4 01/03/2016 31/03/2016
orange CD3 01/03/2016 31/03/2016
pear CD8 01/03/2016 01/03/2016
apple CD22 01/03/2016 01/03/2016

In lets say Cell E1 contains Orange, E2 contains 01/03/2016 and E3 contains 31/03/2016. I need the formula to look up E1 within the table and if it finds E1 (ie Orange), then to see if E2 & E3 match Columns C & D respectively, and if so then return the associated code in Col B. As you can see, there could be multiple answers in which case it needs to just pick 1 code (doesn't matter which).

I thought the best would be a vlookup, then IF combined with AND statements to see if the dates match, and return Code if so. I am struggling to combine this, are you able to help please?

Thank you