Last November I was scheduled for LGA-ORD-RDU-DCA-BOS-SNN-BOS-LGA. Same as you, I had a same day turn in SNN. My Eagle flight DCA-BOS went mechanical and arrived 14 minutes before the scheduled departure to SNN. Even though I got to the gate with 6 minutes to spare, the solitary agent pulled the 15 minute rule and refused to board me, even with the plane still at the gate. Oh, and it did arrive into Shannon 45 minutes early.
I declared the trip-in-vain and booked me back to LGA the next afternoon. She also gave me a dinner and hotel voucher. Being that Tampa was my destination on a separate PNR from New York, and the Boston agent didn't really care, I called reservations. A supervisor in Columbus booked me on the 5:50am to Chicago and onwards to Tampa - all in First with his compliments for the troubles. ^
OK - as far as the refund goes. Apparently someone in DCA printed my delayed Eagle segment out to a paper ticket. No one knows why, and it prevented my electronic refund from going through. Even though I sent a couple e-mails and a snail-mail letter to Customer Refunds explaining I did not have a paper ticket, nothing happened.
Seven months later, AAdvantage CS put me through to the Executive Offices to speak with someone. The person I spoke with said she would contact Refunds and get the issue resolved. Two weeks later I had a $155 refund on my credit card for the BOS-SNN-LGA segments. My original ticket cost $320.
^
As far as getting mileage credit for the flights not flown, a few days after the trip a supervisor at AAdvantage CS said she could not give credit for flights not flown, but did issued 5,000 "customer service" bonus miles. When I explained this trip was to put me over 50,000 miles, she also extended my Platinum status through 2007 with no further questions.
The fun part is I had to call AAdvantage again two weeks later for something unrelated. In the discussion this trip came up. The agent looked through the notes in my file then said, "I hope I won't get into trouble for going against a supervisor, but I'm going to go ahead and post all three missed flights to your account."
YMMV