Starter engages while running & also when no key in ignition
 

2008 Buick Lucerne 75,000 miles, when I started my car after it sitting for a couple days while raining, while it was running the starter engaged and made a horrible sound and the light on dash dimmed, this happened a couple times which made me turn it off and take the key out of the ignition, when I got out of the car - key in my hand- the starter turned on once again for a few seconds , I eventually took starter relay out and the cranking stopped. When I put it back it happened again after starting the car. I read other articles and switched out the relay and had the same issue when the car was running and turned off….. today the air is dry and no rain , I started and drove 50 miles no issues, I am looking to see if anyone else has ever had this happening, I’m interested to see if is the starter solenoid itself or what causes this besides a Gremlin in my engine.