To clarify a little on 3C's post, the $700 is gone, sorry. The only thing left in question is the value of the unused JFK->home ticket which will depend on it's fare class.

This is the danger on flying split tickets. DL has no responsibility for BA's late flight when on another ticket. If it was the same ticket things are different. From DLs point of view, you just did not show up for the flight.

I fly split tickets across the Pacific all the time. But I realize that sometime I will get "burned" by it.

If you want to plead for "symapthy points", I would try BA not DL.