Just quit. Tried to restart, maybe it will and maybe it won't.

Sounds like it's ignition/electrical as opposed to fuel but to be sure, the simplest way to start is with a 'gap type' spark tester. When it dies, and you are trying to restart, see if you have any spark. If you do, it's more than likely fuel related, and if you don't, then you know to look for an electrical/ignition problem.

BTW, the gap type spark tester is a good investment and available at most any auto parts store. Usually they are <$15 and the gap is adjustable. The Briggs and Stratton one is set for a gap of 0.167" but if you adjust yours to anything close to a quarter inch(0.250), you'll be fine.

So, let's start with question 1, fuel or electrical and go from there. Let us know how you make out!