Turns over but why doesn't it start?

Assuming your truck is old enough to have a distributor cap and wires, either one could be shorting out when wet or damp.
You may need to replace the cap, rotor and wires to fix the problem.

plastic distributor ? wrong screws in rotor? timing?

i would replace distributor cap first. cause a little moisture in there can cause misfires, making you feel like your running rough. if not i believe your timing belt and that would need to be checked by mech.

Replace the distributor cap and rotor button. And dont get a cheap cap, get a oem one or it will just happen again.

they are known for burning through the plastic. which causes it to run rough.

Replace the spark plugs and wires along with a distributor cap and rotor. Be careful to leave the old wires and plug wires connected to dist.cap, just remove dist. cap from the distributor and lay aside with plug wires on it then install rotor then new cap and proceed to replace each wire for cap and spark plug one at a time so you don't mix up the spark plug wire firing order. Cap laying to the side is used for reference purpose.

Here are a couple of guesses for things to check: vacuum leak (low vacuum pressure), worn distributor cap or rotor, incorrect timing, clogged fuel injectors, malfunctioning fuel pump (low fuel pressure), ignition module on its way out. I hope these suggestions help you out.

Check your ignition wires, rotor and cap. Backfiring is caused by ignition misfire or worst case, a burned intake valve. Your distributor is locked in place so timing should not be an issue but the pickup inside the distributor may have become loose and then can cause this as well (but happens very rarely)

bro, check ur main relay. its under the dash. replace it, check also ur distributor(replace it). and also your ECU

simply replace distributor cap and rotor button, wires and plugs. that will fix it