Do a Wikepdia search on 'HDCP' to see why this is happening. You basically have 2 options:
1. If your TV also has a component input then use component to the Slingbox and the use the pass-through to use component to the TV.
2. If your TV does not have a component input then use the HDMI, but then you will only be able to send SD quality to the Slingbox using the composite output.
What might bve happening here is that you are running a component (red, blue,green cable & separate audio cables) connection from your cable box to your slingbox and an HDMI connection from the same cable box to the TV. My experience has been that, at least Scientific Atlanta cable boxes, is that you can only have one active output from the cable box, otherwise you might have a tv signal and no signal to the slingbox or visa versa or none. Best way I found was to disconnect one that you are not using, thus allowing the other signal. Or, you can use the component bypass thru the slingbox, which is the RBG cable from the cable box to slingbox, then another RBG calbe from slingbox to the tv. This set up would need 2 red and white audio cables as well.(1 set from cable bos to slingbox and aonother from slingbox to the tv.)
Can understand your frustration, as an HDMI cable is the best and also no additional audio cable is required as both signals are carried by th HDMI.
Hope this helps.
Many cable boxes can only put out hi res picture on one output at a time ...example hdmi only or component only...not both at same time. They can however output one hi res (hdmi or component) and one low res (RF tuner on channel 3 or composite) atbthe same time.
As other user points out, try looping thru component.