Bike doesn't want to start after (or when) it rains

[dyetube]

Got a '01 1500 nomad fi that for some reason whenever it rains (at least 99% of the time) won't turn over. This also can happen in a heavy fog where there is a lot of condensation. It tries to crank but never turns over and I just end up wearing down the battery. Has anyone else ever had this issue? I have a lot of grease on the motor (which I need to clean) and a while back when the dealer saw the grease he told me I probably need work done on the headers (that's what I remember anyways)? Could it have to do with that? Just trying to figure out what could cause this as my bike is my full time ride and I can't have this happen anymore.