Is my mower gonzo?

I have a Servistar (MTD) gasoline-powered push lawn mower, Model #115-074-015, with a Briggs & Stratton 3.5hp engine, Model #90700. It is somewhere around 15 years old. This year it has proved impossible to start, even though I changed the spark plug and put in fresh gas; it runs very roughly for a few seconds, smoking badly, then sputters to a stop. The last time I tried, I noticed there was oil dripping from the muffler, which makes me suspect something terminal in the engine.