I have a Power Kraft mower (Briggs 18 horse). I had to jump it off last time I used it, and I mowed until it ran out of gas. By the time I got more gas, it would only slightly turn over, and it was getting dark. So a week later, I tried jumping it off again, but it wouldn't even make a sound. So I figured the battery was just too dead. I put a new battery in there, and still, no sound. I've read where people are talking about fuses, solenoids, switches, and starters being the culprit. The solenoid does spark when the two post are connected. Any help would be greatly appreciated.

You may try to rotate the engine by hand COUNTERCLOCKWISE, and remove the dust cover from the starter to see if the bendix gear is stuck against the ring gear.