A first test to make sure the web service is correctly deployed is to bring up its WSDL.
If there is no WSDL, then the web service has not been deployed correctly.
This test can be performed from any browser, before using the web service tester.
You have already performed the test!
If you do not see the WSDL, despite a deploy that looks successful, I suggest taking a look in the application server logs to make sure that everything indeed is as it should.
Also take a look in the administration console of the application server to see that the web service application appears as it should.