Sorry, but there is a way to test the board, but I'll bet the Tech who came out doesn't have access to the tester. They can be purchased, but the cost of the tester really isn't something you want to take on.
I would replace the new board with the old and make sure that the Tech DEBUGS the fridge instead of taking a SHOTGUN approach to fixing it. I would tell him/her that you want your money back for the board that did not fix the problem. A GOOD Technician will be able to debug this issue without part swapping. I've fixed/debugged many problems with just a basic meter and a 12 volt test light probe and I don't even work on the stuff.
-paul