Blinking light means that the router hasn't assigned the SlingBox an IP address. If you have MAC filtering enabled in the routers setup then you will need to add the MAC address of your SlingBox to the list in the router. That way it knows your SlingBox is "authorized" to be on the network.
If you aren't using MAC filtering then I would reset both the router and the SlingBox.
Have you tried to perform a factory reset of your Slingbox ( http://support.slingmedia.com/get/KB-1000038 ), This will wipe out the configuration to the factory preset and allow your Slingbox to obtain a brand new DHCP address from your router if possible.
If you are still experiencing issues with the network light of your Slingbox while using SlingLinks, try the steps from the following links:
There you will find additional troubleshooting steps that can help you on this situation.