Snapper mower problems?

Ok so The mower is a snapper rear engine with a Briggs 9 HP. I assumed the magneto was the problem so I removed it and wire brushed rust off the flywheel and magneto. I reassembled it and it started fine. I shut it down and waited a few minutes then tried to start it again. Nothing. I am not sure what to check next. I know the carb is a bit out of adjustment but it started fine before. I'm not sure now what to check. Could the magneto be bad and just worked for the time I had it running? I'm kinda lost now . Could the magneto be messing with me or should I move on and try the carb now.