Won't start after rainy day. All lights work and radio but won't start.

By stating “All lights work and radio” - that ‘implies’ the battery has power but the starter will not turn (CRANK) the engine so the engine will then START.

Won't crank...just silence. But after I take key out there is a slight clicking noise in engine for about 10 seconds

Have you tried a jump start when this occurs?

ANYTIME an engine will not CRANK > The first thing to do is try a jump start! The lights and radio working has on bearing on the battery having *enough charge* to operate the starter motor so the engine will CRANK... The fact the accessories are still functional only means the battery is not ‘completely dead’ .. Good luck with it!