Same exact problem with my 2007 J.D. 2305, however I called the John Deere Headquarters in Moline, Illinois and talked to one of their V.P.'s of marketing to try and fix this two year old intermittent problem once and for all.
I told him that I've been trading with J.D. for 50 years now would rather not switch to Kubota or Mahindra at this point. He told me, "We don't want you to do that", and told me to go out and shoot a video with my point & shoot camera of exactly what is happening, ie; the tractor turns over, runs for 2 seconds and then dies...
It has been doing this intermittently for two years now, however, this time appears to have died as it has been sitting out in the driveway now for the past 4 days and will not correct itself this time. So I sent him a one minute video showing that the PTO switch is in the 'off' position, the gear shift lever is in neutral, and that the brake is locked as it should be for starting the tractor.
ONE DAY LATER, I get a call from the John Deere Augusta, Georgia plant (where the 2305 and other compact tractors are made) where one of the trouble shooting experts who viewed my video was and kindly called me.
It turns out the problem here fella's has nothing to do with the safety switches, fuel pump solenoids, the fuel pump, the fuel pump solenoid shut off switch (didn't even know they had one of those), but instead, and I am quoting here from his email to me:
"After watching the YouTube video, I would suspect that the V4 diode is failing or there is a circuit issue with the V4 diode. - Please Refer to Technical Manual "TM2289" pages 144-148 for testing and resolution of the V4 Diode, and this should remedy the problem you are having with your J.D. Model 2305. - Kindly note that the dealership can open a case with their dealer technical assistance center for additional help here should that be necessary."
Hope this helps guys... Happy Fourth, 2013...!!!