I have a 6 y.o. Troybilt riding mower with a 19 hp B&S engine. When I
try to start it, it wouldn't start but was able to jump start.
However, it runs very rough with lots of smoke for a few seconds and
then stops. I can repeat the same thing again.

It seemed fine the last time I used it a week ago. I do change oil
(synthetic) and filter at end of every season, and I have only 1/2
acre to cut once a week. What could be the problem? Is the engine
blown? I never changed the spark plug but it doesn't look like a spark
plug problem does it?