Display goes black when diagnostic test is launched

Your liquid damage has continued to corrode your logic board. You’ll need to take the logic board out and do a detail inspection looking for discoloration, green or white powder (salts). All of this will need to be cleaned off and as needed replace damaged components and traces.

Here’s the guide you’ll need to follow MacBook Pro 15" Retina Display Early 2013 Logic Board Replacement you’ll need a soft paint brush to first dust out the system and use a can of can’ed air to blow away the loose debris. Then get some cotton swabs and distilled water, don’t use tap! To wash the areas you find corrosion. Take detailed pictures of the areas you find.

You may end up finding you’ll need to just replace the logic board.