Intermittent starting problems

Recently, my rtv has decided to start whenever it feels like it. Sometimes it clicks, like the battery is completely dead. If I keep trying the key, it will eventually start and there’s plenty of power to the starter. I’ve also begun to hear what sounds like a small compressor motor running, just behind the drivers seat, AFTER I turn the key to the off position to try another start. This seems strange to me, since nothing should be working when the key is in the off position, right? I’ve also noticed a significant amount of white oxidation around the battery terminals. Ground strap issue you Think?