Engine quits in damp/wet weather

1995 Country, 180,000 miles, 4.0L, 4wd. Great shape.

Over the past few months, when I crank my engine cold, it starts fine, runs for a few seconds then quits. I have to crank it quite a few times till it starts again. I have to give it gas and run it at a faster idle or it will quit. It does this only when it is raining, has recently rained or is very damp outside (like early in the morning). After it has warmed up, it runs fine. Have replaced plugs, wires, rotor and cap (it was due anyway...but no difference before/after). Also replaced fuel filter. Everything is stock. Any ideas?

My guess was going to be the plug wires since I have heard of that happening before but it seems you already eliminated that possibility. Have you run anything like STP fuel treatment through your tank? Perhaps some water creeped in?

Clean your battery terminals and any grounds.