If you are running your cabling out of the Yellow video output of your set top box and you are only seeing video when the cabling is plugged into the Green Input of the Slingbox, it sounds like you are configured for Component, rather than Composite. This would also be why you are only seeing Black and White video; the Component side needs Red, Blue, and Green to provide a full color picture. You can reconfigure or add a video source using the steps within this article:
Before you do that, you will just need to move the cable that is currently sitting in the Green Input into the Yellow Input.
I hope this helps!
Sling Media Technical Support