96 Achieva shuts off while driving & no start

This problem only happens in the winter. I've been dealing with this for the 2nd winter now. Thus far I have, replaced the ignition switch and put a switch on the passlock to bypass it. What I have noticed is though, the car WILL NOT start until the amber light on the automatic shifter (gear selector) console lights up. What ever powers that up is failing, it causes the engine to just crank. Once the shifter light turns on (5-60 minutes) , it turns over and runs no problem. Can anyone help? Thank you!