Exception you are getting is happening because you downloaded "javax.ws.rs-api-2.0-m09.jar" this jar doesn't have ProcessingException download the latest one
Class not foundCaused by: java.lang.NoClassDefFoundError: javax/ws/rs/ProcessingException
Download this jar javax.ws.rs-api-2.0.jar
<dependency>
<groupId>javax.ws.rs</groupId>
<artifactId>javax.ws.rs-api</artifactId>
<version>2.0</version>
</dependency>
Secondly I think you are missing a part from your web.xml
Try adding these things to your web.xml as appropriate for you application. If you don't have this section this may also lead to SEVERE: A child container failed during start....
This is what you are missing. Please note that param-value is the list of packages that contain your rest services.
<servlet>
<servlet-name>jersey-serlvet</servlet-name>
<servlet-class>org.glassfish.jersey.servlet.ServletContainer</servlet-class>
<init-param>
<param-name>jersey.config.server.provider.packages;org.codehaus.jackson.jaxrs</param-name>
<param-value>com.your.package.for.rest</param-value>
</init-param>
<load-on-startup>1</load-on-startup>
</servlet>
To get latest Jackson use this Link
<dependency>
<groupId>com.fasterxml.jackson.jaxrs</groupId>
<artifactId>jackson-jaxrs-json-provider</artifactId>
<version>2.3.3</version>
</dependency>