On most cars a neutral safety switch prevents the car from being put into gear unless the brake pedal is depressed. I don't know what is used on an '04 Dodge diesel, but a buddy had to replace two or three on his Jeep over a 5-7 years span, so my confidence is low on chrysler electronics.

Research "Neutral Safety Switch" for your make and model and hopefully it is somewhere easy to get to. Some are internal to the transmission. It may be easy to remove and clean out the grime, and check for continuity with a multimeter. Or it may need replacement, if it is internal to the transmission, $$$ repair job.

Good Luck!

-T

There is a shift interlock soleniod on the left side of the steering column. It locks and unlocks the lever on the shifter. It is powered by fuse 22 in the engine bay rear left. It is connected to the computer bus, brake pedal switch, and ABS. If it hanging up in the cold, it could be the cause.