Here is the Illustrated Parts List:
http://bsintek.basco.com/BriggsDocumentDisplay/18hruJXHnfBhU7y.pdfHere is the Operator's Manual:
http://bsintek.basco.com/BriggsDocumentDisplay/29lpAFKT9FzXFix2.pdfThe engine was made on 17 May, 2002.
The Operator's manual has instructions for starting the engine. We need to see pictures of it. At this point I do not know whether its carburetor has a manual choke, and automatic choke, or a primer. We also need to know what you did between when it started running, and when it stopped running. Did you open the choke, or move the speed control?
If you can feel substantial compression by putting your thumb over the spark plug hole, it is unlikely that lack of compression is keeping it from running, especially after it started easily.