02 Dodge Ram 1500 5.9L when the truck is parked and gets wet underneath the truck won’t start?

does the top get wet?

Yes everything gets wet

Possible distributor cap,Bad wires. they don't like dampness.

I bought 'ol blue in Texas but lived in upstate NY for 5 years and had similar problems. The first thing I'd try...is check all the connectors that have anything to do with the ignition...clean them. Next, remove the ignition coil n do a close up physical inspection to see if it's cracked or arcing. If it is...replace it. Some may shriek in terror here, but if water n the distributor is yore problem, here is a simple solution. The distributor takes a full time contortionist to get to, but if you pull the cap n spray the inside with electronic spray or brake cleaner, there's a hole at the bottom for the liquid to drain. Replace the cap, rotor and pick up coil whilst you got this beast apart. Once it's all back together, before you put the cap back on, run a thin bead of silicone between the cap n distributor base n screw the cap down. If water/moisture getting into the distributor is yore problem this will cure it. I did this n the only time I mess with my distributor is to do routine maintenance. Also, check the seals around the hood area near the fresh air intake where the wipers are n make sure the weatherstripping is sealing properly.