Your EntityManagerFactory doesn't get properly created at initialization time (so it is null), hence the NullPointerException when you try to use it to obtain an EntityManager.
And while EclipseLink should certainly not fail with a NPE while trying to generate an internationalized message for the exception (you should log this as a bug), the trace still contains useful information, as shown in bold below:
[EL Severe]: 2010-10-23 05:27:14.092--ServerSession(1673653)--java.lang.NullPointerException
at java.util.ResourceBundle.getBundle(Unknown Source)
at org.eclipse.persistence.exceptions.i18n.ExceptionMessageGenerator.buildMessage(ExceptionMessageGenerator.java:47)
at org.eclipse.persistence.exceptions.DatabaseException.unableToAcquireConnectionFromDriverException(DatabaseException.java:376)
at org.eclipse.persistence.sessions.DefaultConnector.connect(DefaultConnector.java:91)
at org.eclipse.persistence.sessions.DatasourceLogin.connectToDatasource(DatasourceLogin.java:162)
at org.eclipse.persistence.internal.sessions.DatabaseSessionImpl.loginAndDetectDatasource(DatabaseSessionImpl.java:579)
at org.eclipse.persistence.internal.jpa.EntityManagerFactoryProvider.login(EntityManagerFactoryProvider.java:228)
at org.eclipse.persistence.internal.jpa.EntityManagerSetupImpl.deploy(EntityManagerSetupImpl.java:380)
at org.eclipse.persistence.internal.jpa.EntityManagerFactoryImpl.getServerSession(EntityManagerFactoryImpl.java:157)
at org.eclipse.persistence.internal.jpa.EntityManagerFactoryImpl.createEntityManagerImpl(EntityManagerFactoryImpl.java:214)
at org.eclipse.persistence.internal.jpa.EntityManagerFactoryImpl.createEntityManager(EntityManagerFactoryImpl.java:202)
...
There is very likely something wrong with your connection pool configuration, EclipseLink isn't able to get a valid connection from it.
I can't give a more precise answer without more details about your settings like the persistence.xml, the Tomcat datasource configuration, the way you use Derby (in server mode?). But that's where to look.