I had similar issues. For me, cold start was normal, hot/warm starts was either off or on. In my case it was the Cam and/or Crank sensor. I replace both at the same time, so I can't say which one fixed it. I think what happens is that the ECU misses the first couple ignition trigger events, but is ok with spraying the injectors and it quickly floods out. When you roll start it, the ECU doesn't see the starter signal and doesn't send the initial priming pulse.
-Rob