Well, I guess it comes down to this: the airline has done nothing wrong and is fulfilling its side of the contract. You're asking NW to break the clearly-defined rules to suit your specific situation--which it is in no way obligated to do. Plus, the favor that you're asking for doesn't fall within general precedent--i.e. the passenger is not the person experiencing the medical crisis.

Unfortunately, if your ticket is indeed non-changeable and non-refundable, I'd use this as a lesson learned and rebook another ticket as you see fit. It seems evident that they've taken a stand and are unwilling to change despite your circumstances. Is it the "right" thing to do in your or my mind? Debatable. But these are airline rules and they don't necessarily fall within the general realm of common sense.

Sorry.