Intermittent Start Problem

LS model with a 3.0 Duratec Engine.
Intermittent start problem no codes generated and no other drivability problems

So Far I:
• Checked inertia switch (in trunk) with meter.
• Supplied twelve volts power to down-stream side of inertia switch – fuel pump runs.
• Replaced fuel filter
• Replaced power control module (PCM) relay.
• Replaced Fuel Pump Relay

When car starts – turning ignition key just before start position – fuel pump runs (can be heard running) – car starts.

When car will not start – turning ignition key just before start position – fuel pump does not run (can not be heard running) – car does not start.

When car will not start – switching the ignition key on/off several times (removing the key from the ignition switch each time) will eventually get the fuel pump to run – and the car will start.

I believe this problem is either a bad fuel pump or power control module (PCM).

How can I determine which component is faulty and causing the problem?

If you feel it may be a different problem – please let me know what it might be.

Thank You.

John Lipps