in server.xml I\'ve defined global resource (I\'m using Tomcat 6):
   
          The <non-jta-data-source> in persistence.xml should be
java:comp/env/jdbc/myds
as per the response in http://forums.oracle.com/forums/thread.jspa?messageID=1899677
And also is your db driver in $CATALINA_HOME/lib
Did you make that resource available for the application by declaring it in your web.xml?
<resource-ref>
  <description>DB Connection</description>
  <res-ref-name>jdbc/myds</res-ref-name>
  <res-type>javax.sql.DataSource</res-type>
  <res-auth>Container</res-auth>
</resource-ref>
(Im using Apache OpenJPA library in Tomcat7 so may not match to Hibernate stuff)
I have never used a global jdbc for my OpenJPA webapps but gave it a try. It worked and this is my configuration. See folder where persistence.xml is saved, probably is openjpa problem but without it nothing works.
myapp/WEB-INF/classes/META-INF/persistence.xml
this is using openjpa provider so class list may not be needed in hibernate.
<?xml version="1.0" encoding="UTF-8"?> 
<persistence version="1.0" xmlns="http://java.sun.com/xml/ns/persistence" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<persistence-unit name="main" transaction-type="RESOURCE_LOCAL">
    <provider>org.apache.openjpa.persistence.PersistenceProviderImpl</provider>
    <non-jta-data-source>java:comp/env/jdbc/mydb</non-jta-data-source>
    <class>com.myapp.db.User</class>
    <class>com.myapp.db.Server</class>
    <properties>
        <property name="openjpa.DynamicEnhancementAgent" value="false" />
        <property name="openjpa.RuntimeUnenhancedClasses" value="unsupported" /> 
        <property name="openjpa.Log" value="commons" />
        <property name="openjpa.ConnectionFactoryProperties" value="PrintParameters=true" />
    </properties>
</persistence-unit>
</persistence>
tomcat/conf/server.xml
Add global jdbc resource.
  ..cut...
  <GlobalNamingResources>
    <Resource name="UserDatabase" auth="Container"
              type="org.apache.catalina.UserDatabase"
              description="User database that can be updated and saved"
              factory="org.apache.catalina.users.MemoryUserDatabaseFactory"
              pathname="conf/tomcat-users.xml" readonly="true"  />
    <Resource name="jdbc/mydb" auth="Container" type="javax.sql.DataSource"
        maxActive="100" maxIdle="20" maxWait="10000"
        username="myuser" password="mypwd"
        driverClassName="com.mysql.jdbc.Driver"
        url="jdbc:mysql://localhost:3306/mydb?useUnicode=true&characterEncoding=utf8"
        validationQuery="SELECT 1" removeAbandoned="true" removeAbandonedTimeout="300"
    />
  </GlobalNamingResources>
  ..cut...
tomcat/conf/Catalina/localhost/myapp.xml
this my development box so I use docBase to link directly to projects folder. You should be find inserting this to war package (META-INF/context.xml) when deployed to production box.
<?xml version="1.0" encoding="UTF-8"?>
<Context docBase="/projects/myapp/web" reloadable="true" crossContext="true" >
  <Realm className="org.apache.catalina.realm.DataSourceRealm"
    dataSourceName="jdbc/mydb" localDataSource="false" digest="SHA"
    userTable="user"            userNameCol="username" userCredCol="password"
    userRoleTable="user_role_v" roleNameCol="role" 
  />
  <ResourceLink name="jdbc/mydb" global="jdbc/mydb" type="javax.sql.DataSource" />
</Context>
myapp/WEB-INF/web.xml
Add resource-ref to the end of file.
<?xml version="1.0" encoding="ISO-8859-1"?>
<web-app xmlns="http://java.sun.com/xml/ns/javaee"
  xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
  xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd"
  version="3.0" >
  <description>Webapp</description>
  <display-name>Webapp</display-name>
  ..cut...
  <resource-ref>
    <description>mydb</description>
    <res-ref-name>jdbc/mydb</res-ref-name>
    <res-type>javax.sql.DataSource</res-type>
    <res-auth>Container</res-auth>
  </resource-ref>
</web-app>
Because Im using OpenJPA+Tomcat7 (not fullsized j2ee container) this may look overengineering but thats how it works. Results are good and developing db-aware webapps is very easy. No need to manual sql query hardcoding and oldskool DAO classes.