Hmmmm, that's a toughie!! If you hear the pump whine when ign on and problem still happens then it's nothing to do with the kill switch, but do make sure, you could end up pulling the thing apart for no reason if it was that.
So it's really intermittent? Like, wont neccessarily happen under any circumsatance, but only happens when hot?
If that's the case, it points to the Crank angle sensor being a tweeb (easy way to check this is at ecm connector pins, 18-6 in an 04-05 manual shows how, I assume it's the same, or near enough)? Crank angle sensor or pos sensor, is easiest to check. And it's a single point, where as if it were a coil pack it'd need to be all of them failing at the same time as it's not giving any "kicks" when tryna start it (That's an assumption, but should hold true).
Let us know how ya go.