Turning thermostat to call for cooling gets the blower going and causes a hum outside. Based on my limited knowledge and google skills, it sounds like a bad capacitor is on the short list of things that may cause this. Looking at the capacitor tells me if it isn't bad yet, it will be soon, so I will replace this no matter what. There is no bulge I can see, but it is very rusty. Any thoughts? Also, after carefully noting all wire placement, I figured maybe I could clean corrosion and get it going. As I was taking off the wires the other end of the short jumper came off. I figure it goes to the slightly bent terminal at the top of the switch next to it, but of course I didn't look, notice or take a photo so I am just guessing because it appears worn and used. There is also a place it would reach at the side/middle of that relay, but the contact doesn't look used. Any help you can offer is appreciated. I have a friend who may be able to come over and help so if I find the correct info, I will edit this post for posterity.

Tech comes out last week. Replaces low voltage fuse. Works fine for a week and quits. Now I know where the fuse is located, so I go the auto parts store and buy a pack. Replaced the fuse and it immediately blows. Short somewhere but I don't have a clue where to look. ideas?