I recommend in checking your firewall rules where the Slingbox is located. Make sure that both UDP and TCP ports are being forwarded to your Slingbox's Private IP address. Most of the time this is the reason why people are able to use one device remotely but not another. Usually, people only setup forward the TCP port but ignore the UDP.
If that doesn't work, it could be that your mobile broadband provider is blocking or using that specific port for their own nafarious purposes. You can try to work around that by changing the Slingbox's default port from 5001 to a more common port like 80 (HTTP) or 443 (HTTPS). Just make sure that you also change the port forwarding rules to match the Slingbox's port number if this is necessary.
Slingplayer does not work with the current OS of the 9700 that has been updated a few times since the sling media application was created for the blackberry.
Read about the issues here: