Depending on the size of the company you work for, they may have a benefit person who manages the benefit programs. Find out who it is and plead your case with that person, find out whom your boss was suppose to turn the form into and contact them directly if at all possible.
Hope this helps,
Do you have copies of the signed dated application? If so, definitely go to the Big boss! And, state the verbal your boss gave you. You did what you had to do - you turned in the paper in a timely fashion, and they did not do their part.
Look them in the eye and ask them "What are you going to do since you did not submit this ontime?"