Assuming that you are using component cables to connect your cable box to your SB, then an all-green screen suggests to me that your component cables are faulty and only the green signal in the trio of red-green-blue video signals is being delivered to the SB from the cable box. I would first try a replacement component cable connected directly from the cable box to the TV (with the SB out of the wiring loop) to confirm that the cable is good and the TV does not display a green screen. Do that with both of the component cables you will be using in your setup (one between cable box and SB, and the second between the SB and the TV). If both component cables work correctly without the SB involved, then try connecting again the SB into the loop. If it doesn't work correctly now, then I suspect that the SB itself is faulty.
What I'm getting from your post, is that you're having problems with the Slingbox video signal.
In this case, you can start by reset the Slingbox.
Also, you can try a different set of Audio and Video Cables and even a different Audio and Video Source such as a DVD, that way, you can discard the current one as the potential issue.
Besides that you can check the following link