I came here with a very similar issue.
My 2002 3.7 didn't want to start, despite having a good charged battery, with the starter just engaging and disengaging as I turned the key. Eventually got it started with help from an addition battery with jump leads, and a boosted pack.
Something is taking voltage with the ignition ON, which I suspect is the factory Premium Alarm/Immobiliser which has a flat internal battery.
Anyway, I connected by OBD reader to check the system voltage, with the engine running, and it was sitting stable at 14.2-14.4V at idle.
However, my reader also shows, by default, live data for Coolant Temperature and Throttle Position sensors, and these are anything but stable.
The Coolant Temperature gauge display was swinging like a windshield wiper, between +90C and -38C!
All the time the dash display for temperature was stable, just over mid-point.
The throttle position sensor display was also swinging wildly, between 4% and 35%, although the idle revs were perfectly stable at 600 rpm.
This makes me thing that the issues are unlikely to be those sensors but more likely to be an electrical problem with their connections to the ECU, or something within the ECU itself.
This car went through a phase a few years ago, with random CEL codes, mainly related to the 4 O2 sensors, but also random other stuff, which was "cured" by fitting a fat wire direct;y from the battery negative terminal to the earth bonding stud on the firewall. This was initially fitted just for faultfinding but was so effective that it became permanent.
This time there's no CEL, just these bizarre readings from the ECU.
Anyone any ideas?