are you sure the power led is blinking? if yes, then most likely it means that the box is not getting enough juice from the psu adapter. because the network led on the slingbox is not on, the network led on the slinglink connected to it is also not on. that is understandable. which model of the slingbox do you have?
So if I understand correctly, the power light on your Slingbox is blinking?
With that being said, it sounds like it could be a power issue.
I would advise you to Contact Sling Media Support, at 1-877-go-sling to further trouble shoot your Slingbox.
Best of luck,
Sling Moderation Team