As the others stated, check the JDBC connection and drivers. If it is a driver issue, the VSE.log and/or VS_<theServiceName>.log might have some helpful clues such as a class not found exception, connection refused exception, duplicate key, etc.
When you say the service works "without the JDBC step" in the model, is the JSR-223 step also removed?
If "yes", meaning the JSR step is also removed, double check that the JSR step is not throwing an exception during processing. An exception in the JSR step translates to an environment error which can cause the service to abort.