I understand that you are having some issues with the Slingbox PRO since you are not able to get the connection to the Internet.
If the lights on the Slingbox blinks, it means that the connection to your network is not good enough. In all case, I recommend you to check the following links and follow the indications:
Regarding you last question, the SlingPlayer for iPhone application will work only if you have a Slingbox SOLO or the Slingbox PRO-HD. The following third-party link will provide you with all the details about this application: