So, did you merely get rid of it?
-Same issue on mine; '06 3.5 FWD, 120K. Issue was highly intermittent until it just died: Cranks, but only rarely fires. When cold, it might start to rough idle until dying after a minute with no restart.
ODB II seems to have poor reporting for this common issue, with only a single P0336 related. I went ahead and swapped out the *IMPOSSIBLE* CKP (you have to be a contortionist!) with no improvement. I had previously replaced the fuel pump (with integral filter) because the schrader had no fuel pressure; before finding that the schrader is on the fuel vapor return line! 🦧 -Though the pump did test weak and WAS rusty, and the tank had about a pint of dirty water in it. BTW, the tank had to be pried down since double-stick foam pads used in assembly had kinda glued it in place.
I am now testing the ignition control module, but my '06 3.5 module does not resemble the pictures: My coil towers arranged so plug wires are 2-rear, 2-front, 2-rear, instead of all six in a row.
Anyone have a pinout diagram for this alternate module?
If the module tests okay, then the self-destructing wiring, or the ECM, is all that's left.