Let's quickly run through the basics here to make sure everyone's on the same page:
1. Check your router- write down the network you're using (i.e. the network addressing scheme you've got on your internal network). Check your DHCP options and find out what range of IPs are being assigned by DHCP. Check your port forwarding and make sure that you're forwarding 5001 to the IP address you're going to assign to the SlingBox using standard port forwarding, not port triggering. Are you doing port forwarding to any other PCs and/or do you have any other ports "open"? I've heard of Netgear routers having issues trying to forward ports to multiple computers.
2. Go into the SlingBox and check its network properties. Are you assigning it a valid (on your network) IP address that's NOT in the DHCP range? You should be. Make sure you've got the subnet mask entered correctly AND the default gateway (the internal IP address of your router).

If I'm not mistaken the 192.168.1.237 address you spoke of earlier (being assigned to your SlingBox) is also the IP address they assign to the Sling in their online manual pages. I'm assuming that since you can view the Sling within your home network you've got this right, but double check it. Make sure you've got the default gateway set on the Sling...without it set correctly you'll be able to view it locally but it won't know how to get out to the world at large. Does the SlingBox indicate that it's registering with SlingFinder correctly?

Just a thought here...does your Netgear have a DMZ?