It sounds like you are having the same exact issue this support article talks about. It says "The power light is on, and the Slingbox logo is fully-lighted. But the network light is off. What can I do?" Then lists what be wrong. Going with this, I would recommend purchasing a new power supply adapter.
Below is the article I referenced, and a link to purchase a new power supply:
- My Slingbox won't connect and won't reset; all lights are on except the network light
- Replacement Parts
Sling Media Moderation Team
Just get a new power supply adapter. That happened to me two weeks ago so I did a quick serch on the web it turns out my power supply wasn't working as good as it did once. That new power supply fiexed my Slingbox PROHD. here is where I got mine http://http://www.slingbox.com/go/buy-replacement-parts just make sure you choose the right one. (Slingbox PRO-HD / SOLO Power Supply).