I understand that you are having some issues in order to determine if your SlingLinks are working in a proper way.
Although you have already applied some of the recommended steps, I encourage you to pay special attention to the following steps:
SlingLink (or powerline ethernet adaptor set)
1. Make sure that they're are not plugged into power strips, or into outlets that have power strips plugged into them.
2. Check that the Link light (or other connection indicator) is on. This should be the case with both on the adaptor that's connected to your Slingbox and with the one that's connected to your router. If the Link light or connection indicator is not on, the two outlets may be on different circuits in your home (this is very common with most homes today). There may also be an issue with the SlingLink or powerline adaptors themselves.
3. To check that, plug the adaptors into two outlets that are near each other. See if the Link lights, or connection indicators, come on. If they don't, then the adaptor set could be malfunctioning. If the Link lights or connection indicators do come on, then the solution for your Slingbox and router is going to be trying different outlets until you find a pair that works for the SlingLink (or other powerline adaptor) that's connected to your Slingbox, as well as the one that's connected to your router.
To really make sure your SlingLink set or wireless bridge isn't the problem
It's ugly, it's inconvenient, and it's unsightly! But if you really want to be sure that your SlingLink or wireless bridge is (or isn't) the problem, the best way to do that is to move your Slingbox temporarily near your router. You don't have to worry about connecting it to your A/V source (for example, your cable or satellite box). You're only interested in what the Network status light is doing.
Take a known good Ethernet cable and connect the Slingbox to your router directly. Once this is done, plug your Slingbox into the power outlet.
If with this simple direct connection the network light is still blinking, then the issue is either the Slingbox or your router.
If that's the case, your last step is to try resetting your Slingbox, as explained below.
Make sure to follow these recommendations (available through the website at www.slingbox.com) and let us know how it works.
I don't understand the relevance of what you have written. Do you believe that the SlingLinks might be functioning normally, even though when both are plugged into the same outlet, as per the troubleshooting instructions that you reposted, that the Link light on one of them is blinking; and the other is steady on?