Starting problem

Sounds like u have bad ignition switch I would have the codes check in ur body control module if u have ethier a b3033 or b2960 or both replace the ignition switch they have changed the design of that switch atleast 3 times pretty common especially in cold weather. Let me know how it goes.
Louie

Does the security light flash while it won't start. I can't be 100 percent sure but I recently fixed one that had a faulty ignition switch. Take it somewhere to have it scanned for codes. That should pinpoint the problem.

Bad ignition switch is really common for those cars causing the no start's then start's to happen. Take it some where that can read your body control module code's. If you have a code B02960 and or B3033 then replace the ignition switch and you should be good to go.

In tank fuel pumps are cooled and lubricated by the fuel in the tank. When you run a car out of gas, it pumps a lot of air through the pump which overheats it and causes some severe wear and many times, failure when they cool off.
You will need to use a fuel pressure gauge to verify this

So when it won't start is the security light on solid or flashing?If so most likely you have a bad ignition switch. Let me know so we can talk about it.

Then you need to have your body control module scanned for code's and if you have a B2960 and or a B3033 then you have a bad ignition switch. Really common on that car.