Try performing a factory reset as described in this article (http://support.slingmedia.com/get/KB-1000038). It'll wipe out any configuration information that might be interferring with it accepting a brand new DHCP address.
You can also try another port, cable, or different router... however, as I understand I understand it is not entirely uncommon for malfunctioning AC adapter to also cause the symptoms that you've described. On the bottom of the Slingbox, you should see the power requirements; voltage, amps, and polarity. If you have a compatible power supply then you can test it with your Slingbox to see if there's any change.