2003 Volkswagen Jetta Car only runs when dry out and if wet

I have an 03 Jetta that when its wet and moist out it runs extremely rough and sometimes won't start. But when it is dry out it is quiet, nice, and runs how its suupose to. The battery also drains when left hooked up unless its nice out as well. In need of some help asap because as of now I have no vehicle. The motor and tranny are all good and replaced though and the coil pack is also good I was told. I was told it would have to be electrical ground wiring somewhere needs replaced but don't know. PLEASE HELP