Small Engines (Lawn Mowers, etc.): Briggs 17 HP OHV Smoking, craftsman riding lawn mower, briggs stratton engine

Question
I just bought a used Craftsman riding lawn mower for $500.00. Model #917270722. Serial #062698D003730. The serial plate was missing from the Briggs & Stratton engine, but it's a 17 HP turbo cooled OHV engine. After using it twice to mow, the engine started smoking really bad (grey smoke) and it just quit. Now, I can't get it started. Any idea what could be wrong? I know nothing about engines, except keep the battery charged and the spark plug clean. I sure hope I haven't been screwed on this deal. Does it sound bad?

Answer
Your engine model according to the Sears model number is 311707-0132-E1.

Is there oil in the engine?  Is the oil level correct?  Does the oil smell like gasoline?

First thing I would do is start with a fresh oil change, use SAE-30 oil.
Does the engine have compression?
Let me know.
Eric