You can check that the alfresco webservices are accessible on a remote machine by accessing the url http://hostname:8080/alfresco/api.  You should get the following message.
Axis HTTP Servlet
Hi, you have reached the AXIS HTTP Servlet. Normally you would be hitting this URL with a SOAP client rather than a browser.

In case you are interested, my AXIS transport name appears to be 'http'

To access a remote web service instead of a local one in your code you need to add a file called webserviceclient.properties to the classpath

webserviceclient.properties
repository.location=http://hostname:8080/alfresco/api

If you’re accessing the web service from your own web application then you need to place webserviceclient.properties in WEB-INF/classes/alfresco/webserviceclient.properties for it to be picked up properly.