We live in the Pacific Northwest. NW corner of Montana. Very similar weather to Seattle. Every time it rains and I forget and leave the truck outside instead of inside the garage, it will not start. It is a 2001 Dodge Dakota pickup truck. It tries to start but will not fire. I have to sit around and wait for a few dry days and full sun - which is hard to find around here other than August and September. I have had it towed to several different mechanics for review. They have all done the same thing - can’t find anything wrong so they leave it sit around the lot for two or three weeks until the sun shines then charge me a hundred bucks or so for their diagnostic time and a jump start. Every once in a while out of shear frustration, I have it towed to a new mechanic or one of the previous ones but still get the same results. Does fine in the winter with snow, but it has even done it on occasion when going through a car wash - which I know longer do as I am too old to be pushing a pickup out of a car wash.
First suspect would be a coil or ignition related part. You might try taking a windex bottle filled with water, at night with the engine running, spray water on the coil and around ignition components (carefully so you don’t get hurt). Look for sparking or rough running to isolate the bad component.
I am guessing that your truck has a 3.9L engine and your cowl to hood seal fell off. I often find these seals lying on the engine, this will allow water to drip onto the distributor.
Was the shop unable to duplicate this problem with a water hose? If they had to wait two to three weeks for your truck to start so that you could pick it up I think you took it to the wrong shop.
In the picture below you can see the cowl seal resting on the master cylinder.
Like Nevada said, could be water intruding into your ignition system. When at home, run a garden hose over the truck and then see if it starts. If not, see if there’s water on the distributor.
BTW, what town do you live in?