Let's start with a few details of your engine. Being a 92502, it is 9 cubic inches (148 cc, as Mr. Davis said), a third generation design, it has a vertical crankshaft and a VacuJet carburetor, and it has a horizontal-pull starter. You can find out much more than you will ever want to know about it, and other non-current Briggs and Stratton engines, by reading the relevant parts of the Briggs and Stratton engine overhaul manual, here:
http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_70.htm
The "70" at the end of that URL controls page number: 70 is the first page, and there are 224 more following it.

Concerning the specific issue of the ignition, suddenly having no ignition is usually due to the kill wire (wire from ignition module or breaker points to a contact under the governor, operated by the engine speed control) being permanently grounded due to something being bent or mangled somewhere. Whether or not it is the source of your current problem, if your old breaker-point style coil has rusted and delaminated, it may be time to replace it with the post-1982 Briggs ignition system, which they called Magnetron (a strange choice: a magnetron is the radar transmitting tube also used in microwave ovens as the source of Super-High Frequency radio waves. The magnetron was invented in Britain early in WW2, and was a significant new military technology since it made radar possible.) You should be able to get a second hand Magnetron ignition unit from a nearby scrap B&S engine, or a dealer if you know one who doesn't charge too much for commonplace old parts. You can get the official B&S bulletin on how to fit a Magnetron to a breaker-point engine here:

http://www4.briggsandstratton.com/miscpdfs/RNT/magnetron_retro-fit.pdf

Joe Carroll's way of doing this same job seems less complicated, but achieves the same outcome. Note that the Magnetron is a one-piece unit that replaces the old ignition coil. It looks just like the coil except it has a little black plastic bit added inside the iron part on one side. The black plastic bit includes a magnetic sensor that triggers when the flywheel magnet passes by the coil.

It is not necessary to fit a Magnetron - you can just replace your rusted coil with one from another contact-breaker engine. You will need to test or replace your condenser, clean the points, and set them to the correct gap of 0.020" at their point of widest opening. Also test the connecting wires to ensure they are not grounded due to the insulation getting cut through, and look for oil in the little tin box surrounding the breaker points. Oil usually gets in there by leaking past the plastic plunger that opens and closes the points: the other end of the plunger is inside the engine and is swimming in oil. If the plunger is letting oil past, you can try a new plunger and see if that stops the leakage, but if it doesn't, there is wear in the aluminium crankcase around the outside of the plunger, and it would have to be reamed and bushed to stop the leak. This is not worth doing unless you are a collector working on a rare engine: just forget it and fit the Magnetron.

Remember to set the gap between the coil and flywheel to the correct amount (about 0.010", or the thickness of an ordinary business card). An overly large gap will give weak ignition. Too small a gap may result in the flywheel touching the ignition unit.

Concerning your horizontal-pull starter, read this page of the repair manual:

http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_163.htm

The preceding and subsequent pages will also be useful to you in maintaining this component. The main issue is lubrication - the cavity where the balls sit, and the sprags that lock the balls, must be clean and dry or the balls will stick. However the center of the stationary part that includes the sprags, runs on the crankshaft extenstion, which is running at around 3,000 rpm most of the time so it requires some lubrication. Unfortunately unless the lubricant is kept strictly to the outer surface of the crankshaft/inner surface of the stationary part, it will end up spreading to the outside of the stationary part, get on the sprags, spread to the ball compartments, and gum up the works. B&S therefore say use just one drop of good quality oil. If you ever hear a shrill screech from your engine, stop it immediately and service the starter (clean it and oil it). See why I prefer the vertical pull starters?

If you have any problems in following all this, or there are other issues with your engine, just post them in this thread and we'll see if we can help further. Reports on progress, and some pictures, would be useful in making this thread a help to other members.