There are 2 problems listed but only one most important so far. The engine can't start until it gets turned over by the starter. You have to have a hot battery, good battery cable connections, a good starter relay and a electrical circuit from the inginion switch and other circuits to the relay.
Is it a new starter motor? It may be incorrect.
crank sensor is bad
If the car turns over, gets gas and just will not start try the ignition module. CAR TURNS OVER
Check fuel and fire. Pull a plug and smell for raw fuel, and check the plug and see if there is fire to the plug. If I checked the plugs and it is not getting fire or fuel at all what could cause that problem.
It's most likely the electrical system, and it sounds like the moisture is causing a short somewhere.
bad spark plug, bad connection, low battery.
check if it is getting fire
Need a little more info. Is it trying (but failing) to turn over? What's it doing? has new battery and relay. just filled up the gas tank, it turns over and turns over, but wont fire. ends up wearing the battery down. even with a battery charger it wont fire.
when you changed the filter did you prime the fuel system ? this is usually done on the top of where the filter screws on !
Is it a new starter motor? It may be incorrect.
If it turns over sluggishly - could be a bad starter If it turns over normally - fueld could be atomizing too early (Vapor lock)
is it getting gas ? do you have spark?
Start looking at fire and gas. Trace these two that are the main problems.
Check and clean your spark plugs that might be the problem.
crank sensor is bad
In most cases, the engine will not fire or start if the clutch switch is bad. The key will turn in the ignition but there will be no turn-over or sound from the engine. If the engine turns over but doesn't start, there might be a problem with the fuel supply.
If the motor turns over then start by checking for fire at the plugs. Check to make sure that the timing belt is not broken and is working properly. Check the cam and crank sensors for proper operation, as well as proper fuel flow.