I brought a 2003 chevy impala six months ago for 4600 dollars with no warranty. About three weeks later I started having engine problems. Now I'm at the point were I have to buy a new motor. What should I do? Do I have a small claims law suit?

I doubt it. You bought the car without a warranty. Did you buy it privately or from a dealer? If you bought it from a dealer you may have some recourse through "lemon laws", though 6 months may be too long to far back on that. If you bought it privately, then you're basically out of luck. Try this for more info: Lemon Law Statutes, Brochures, and Fact Sheets