Auto Parts: Push starting/starting on a hill with a stick shift when battery is dead, oxygen sensor, stick shift

Question
Can you push start a car with a manual that has a prox key with push-to-start in the other sense and by push start I mean if the battery's dead starting on a hill for example and putting it into gear?

Answer
    That's an excellent question.  These automated starting systems are all different.  You could consult the owner's manual or the manufacturer, but my guess is that they will recommend against it.  And, probably, if the battery is so flat that it will not turn the starter, it is probably too flat to energize all the systems that are needed to get the engine running (fuel pump, injectors, ignition, Oxygen sensor heaters, all the other electronics including the ECM, and the instrument cluster).  If I had a handy hill and some friends who didn't mind helping, though, I'd be tempted to try.  I think you would have to hold down the "start" button while you let off the clutch in first or second gear.  Try first gear and if it is too tall to let the engine turn, then use second.  I used to push start my old MGA in reverse 'cause it's a lower gear than first and the car was hard to push from behind due to the shape.  I don't think you can hurt the car doing this, but if it doesn't work after two or three tries I would stop and fix the battery.