I have a 2003 Dodge Grand Caravan. Replaced the battery yesterday, it started right up. Much to my dismay, a few of the electronics in the car which have never given me problems stopped working. The wipers, blower, console, and windows wouldn't work correctly. After about 5 minutes everything except the radio and blower would work. (All the windows were jerky going up as well.)
I live in an apartment in northern michigan and winter is here, so I did this with a head light in a blizzard, in my parking lot. Had to remove fuse box cover to remove battery, and during that time some snow got on the fuse box.

Thought it might be the alternator so I took it to a shop today. we figured out the battery and alternator are fine, but the fuse box is making a clicking sound, particularly over one of the relay fuses.
Another symptom is both the blower and the radio will turn on for a split second, then turn right back off, as long as the engine is running it will do this.

Any tips/help would be greatly appreciate dodgers!

 

Id sugest fixing the fuse box. That sounds like the root of all your other problems.