It seems that you are having some issues in order to get the connection to your Slingbox when using the web-based application, although you are able to get the connection when using the SlingPlayer software version.
The issue is not related to your Slingbox. Otherwise, you would get the same behavior when running the SlingPlayer software. The root cause might be related to the browser in use. With this in mind, I recommend you to check this link in order to check the information about the supported browser versions.