2002 F150 SuperCrew 5.4 V8 4x4 - 84,xxx miles

I have run into a strange electrical issues lately when my truck has been forced to sit out in the rain (bathroom remodel dumpster is in the garage).

When I take my truck out later that day or the next the following happens:

My 4x4 light on the console will flash and I hear the clicking sound it makes when youtry toturn it on.
When the 4x4 light comes on it will turn off my day time running lights, my wipers will not work as well as my power windows until it does its clicks again.
These issues only happen when the truck is in gear. When I put the truck in park or neutral they go away.
Finally I will get 4 to 5 beeps coming from somewhere every once and a while. I know its not the seatbelt reminder because mine is on and buckled. It sounds almost like the warning tones from the national weather service when they are going to make an announcement on the radio. And I know it wasn’t that because I turned down the radio to make sure. It will beep at me once or sometimes 6 to 7 times.

Eventually everything goes away after a few days of dry weather. So I know its a water issue getting in somewhere but where or what is it affecting?

Thanks in advance for your reply.