Help - GMAT

I decided to apply for a MS in Finance in late January. Since I did not take my GMAT/GRE, the school allowed me to submit my application to comply with the deadline, and submit my gmat score later while telling them when I would be taking the test.

Unfortunately for me, many personal things have happened, which have prevented me from taking the GMAT so far. Therefore my application was incomplete until recently. I was hoping to be able to defer my application for another deadline due to these unforeseen circumstances since the school has another deadline in April.

The thing is that the program I applied to, reviewed my application, and has rejected me even if they initially told me that they would not make any decision on incomplete applications. In their letter, it says that appeals are not possible.

I am crushed because they told me that: 1) they do not make any decision until all items are received, 2) I could choose another deadline.

I am planning on talking to the program's people next week. What are the chances that they will accept my GMAT now and understand that my application was incomplete anyway?