That one second burst from the fuel pump is to insure the pressure is up for starting. That will produce pressure in the fuel supply system but it doesn't mean the pump is running during cranking. If the injectors aren't pulsing during cranking there won't be anything to bleed that pressure down. That's why pressure in the system is misleading.
The place to start is by determining if the automatic shutdown (ASD) relay is turning on during cranking. The easiest way to test that is to measure the voltage on the feed wire. That will be the same color wire at all of the injectors. A test light works better than a voltmeter. You should see voltage there for one second, but what's important is if that voltage comes back during cranking. If it does not, suspect the crankshaft position sensor or camshaft position sensor. If you have a V-6 engine, the distributor is the most likely suspect.
Heading out of town soon. Will check back with your progress in the evening.
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Saturday, September 29th, 2012 AT 7:15 AM