First poster, but had to register to assist after what I went through. Hopefully my situation can benefit you! I'm sorry for the trouble, my car too had an intermittent starting issue. Here's the story:
Purchase 07 is350 with rather low miles a few months back. Fall in love with the car. Last week,it started up and ran for about 2 seconds and then died. Check engine light came on and the car wouldn't even crank after that. Had my wife out to try and jump it, nothing doing. Check engine code remained. I wanted to test out the battery before simply taking it to the dealer. The next day I got a multi-meter on the battery, 12.2v. I hop in the car, starts right up and runs. I drove straight to the dealer.
First suspect: Battery ground bolt on the chassis. They say there was a service bulletin about it (or something similar, I forget the exact verbiage). This gets replaced.
I'm back on the road! Car runs and drives great all weekend. Monday night, car starts and runs for a few minutes. As I'm pulling out of my parking space, it stalls out. The check engine light comes on, it won't crank anymore. Call dealer, they say bring it right in so they can reproduce it. I got it towed in right away, though as soon as they drop the car in the dealer back lot I start it up and it seems to run just fine. At this point, myself and the dealer agree the car isn't safe to drive.
Second suspect: ECU. They say the computer was getting mixed signals but they should have it ready with a new one in a day or two!
Third suspect: Fuel pressure sensor failed/failing. This was a day or two after learning it's the ECU. 2-3 days later I have my car back. It hasn't failed me since but I'll report back if there are any further updates.