You may want to connect your Slingbox directly to your router a test; maybe use a different port or cable. A blinking network light is often a indication that its trying to get a DHCP address. If the LED doesn't turn solid then it can't get one.
Btw, the middle light, do you mean the Sling Media logo? As I understand it is not entirely uncommon for malfunctioning AC adapter to cause the symptoms that you've described. On the bottom of the Slingbox AV, 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.