Does your router act as a DHCP server as well?
Perhaps the Slingbox hasn't been allocated an IP address.
I'm having a problem similar to yours and I'm certain my DHCP option isn't allocating IP numbers.
This my own fault because I can't resist dicking about with things.
I have set static IP numbers on all my other devices, however I can't get to the Slingbox to set a static IP as it isn't appearing on the net (where it has been quite happily for about 3 years).
I downloaded a freeware IP scanner called (unsurprisingly) Advanced IP Scanner, this should help you to see if the slingbox has been allocated an IP.
Anyway, just a thought.