You are correct, it is possible you are running into HDCP (High-Bandwidth Digital Copyright Protection) or SOC (Selectable Output Control), from within that YES set top box, which will stop the video/audio transmission as these programs within the set top box shut down any non-TV source to try and prevent the download and distribution of the content. I've linked a video below that goes over these softwares in a little more depth and also discuss how to setup the Slingbox with your Set Top Box to work around HDCP/SOC:
Now, HDCP and SOC have developed quite a bit since this video was posted and some TV Providers will no longer allow Video and/or Audio to be transmitted if there is any HDMI cabling what-so-ever coming out of the set top box. In this scenario, you can invest in an HDMI adapter with HDCP Bypass, shown and discussed in this article:
You may also want to double check to ensure that you did modify the source from Composite to HDMI when you changed to the new Set Top Box. I'll link the reconfiguration steps, just in case. Please note that as you do have to reconfigure the remote when you reconfigure the source, the article title may look a little off in relation:
I hope this helps!
Sling Media Technical Support