I was running my riding mower and all of the sudden the engine cut out. I lifted the seat where the battery compartment is. I noticed that the red cover over the positive terminal had slipped out of place and the battery lead was rubbing against the chassy and it burnt a little, like a weld mark. Is my battery fried? Or is something else fried. When I turn the key, I hear a click, but no cranking or anything? I tried jumping it with a car, no luck.

Hi,
I think it unusual that you hear a click. I would start with the fuse, however.
Peace,
Clarke