welcome to flyertalk.
sorry, but even with a doctor's note or a (fake) death in the family, you'll not be getting your money back. it'd save you the penalty. the coded NONREF on the ticket, as you said 'whatever that means,' means NONREFundable. based on your verbiage, you're a bright guy and i bet you knew that before asking. you'll get a credit to use towards a future flight, minus a penalty. they tell you that when you ticket.
i'm with flyinbob, you can try to write a FRIENDLY letter to whq and see where that gets you. if you blame united for their 'immoral' practices or whatever, you'll get nowhere. if the gods smile upon you, consider yourself lucky, not right.
fwiw, i don't think amex wouldn't have backed you on this one either, as you're clearly in the wrong--they might have given you a temporary credit, but eventually they'd have charged you for the trip.