It almost sounds like you're unsure about the private IP address of the Slingbox. Your port forwarding rules should have both UDP and TCP ports of the Slingbox forwarded to its private IP address. This article will help you determine that information (http://support.slingbox.com/get/KB-005866.html).
When you're outside of your network, you don't want to specify the private IP address. If you're using the IANA private network address; 10.x.x.x, 172.(16-31).x.x, or 192.168.x.x. then they're not routeable on the open internet. Instead you want to use either the Sling ID or the public IP address of your router. You can get that information by going to (http://www.canyouseeme.org) but you will need to be connected to your local network. It will show you the public IP address of whatever network you're connected to at the time. This public address is shared by all the network devices connected to it.
I am having the same problem but I can view mine wirelessly on the LAN but not outside of the LAN. Did those things help you? I am not an uber geek but fairly tech savvy and I have been fooling with thing thing off and on for a few months! I hope someone can help us here. I am using a WRN300. Please help!!!
Once you've setup the Slingbox for viewing locally, its the routers responsibility to allow remote viewing. I recommend that check your router's firewall rules. You'll need to make sure that that the corresponding public UDP and TCP ports and being forwarded to your Slingbox's private IP address. Most of the time this problem is associated by only having the TCP port forwarded.
Sometimes, you have to deal with either the broadband provider or WiFi Hotspot either blocking the ports, throttling the bandwidth, or using them for their own nefarious purposes. You can try to work around this by changing Slingbox's default service port of 5001 to something more common like port 80 (HTTP) or 443 (HTTPS). If this is necessary, then you also need to change the port forwarding rules to match the new port number.
IP address and Port Number: http://support.slingbox.com/get/KB-005866.html
Port Forwarding: http://support.slingbox.com/get/KB-2000068.html
Network Setup Assistant: http://support.slingbox.com/get/network-assistant.html
Manual Changes: http://support.slingbox.com/get/KB-5000126.html
Also, the follow is an website that will help you configure your WRT300N router (http://portforward.com/english/routers/port_forwarding/Linksys/WRT300N/SlingBox.htm).