Unfortunately you're screwed from a refund since its beyond the 24hr refund window. You purchased a non-refundable ticket it seems, and unfortunately the airline will say their terms were clearly available prior to purchase. Your only available option is to see if they will cancel the ticket for a value voucher to use again on another purchase, or move the dates instead. It sucks, but unfortunately thats what you paid for. AA, DL, and UA...etc all offer refundable tickets for purchase. They just cost a little more.
My take is that the fact they aren't transferrable seems to be theft. I should be able to use the amount towards later purchases. Regardless, I will never use AA again; Northwest did this **** 20 years ago, and they're gone.
