There is likely one of two things causing your issue.
The first is that you may be running into a layer of copy protection called SOC (Selectable Output Control). This issue is usually dealt with once the HDMI cable is disconnected from the cable box, but sometimes, a reboot of the cable box is required as well (leaving the HDMI cable out of course). I would try once again disconnecting the HDMI cable from your cable box, and then unplug your cable box for 10 seconds, plug it back in. See if that works.
If not, then the next thing we want to do is make absolutely sure that the Slingbox is configured to get the audio and video signal from the correct source. Basically, if the Slingbox is configured for the composite input (red, white, yellow cables), but the cables you have running to the Slingbox are component cables (red, blue, green, red, white), then you will still get audio from the audio cables, but you will get no video. What I would do is go to setup.slingbox.com, and click "reconfigure video input." Make sure you select the input that matches the cables running between the cable box and the Slingbox. It sounds like you may have done this already, but I thought I would mention it here just to be sure.
Here is an article on "no video signal" to reference:
And here's an article that discusses SOC (it'll be towards the bottom of the article, and don't mind that it talks about the Slingbox 500 specifically):
Hope this helps!
Yes, that did help. There is definitely a SOC issue. When my dad unplugged the HDMI cable and rebooted the cable box, I was able to watch through Slingplayer over the internet once again.
But here's the problem: the pass-through component signal from the cable box, through the Slingbox, and to my dad's TV is not HD. At least the signal that ends up at the TV is not HD. This is a problem, as my dad will not tolerate this. Is the Slingbox SOLO incapable of passing through an HD signal?
The Slingbox SOLO is capable of passing through a signal that is considered HD video resolution through component cables. Here is a brief article you can reference:
If you're not getting an HD signal on the TV, I would make sure that the video format/resolution is set to the highest that the Slingbox can support (if it's less, then it's probably not an HD signal).
I can see you running into a problem if the best signal coming through component cables (1080i, which shouldn't be too different) is something that your father does not consider HD, because I'm sure he was used the signal coming through on HDMI cables. If you still wish to use your TV with HDMI cables, we recommend the use of an HDMI-to-component converter, which will allow your Slingbox to use component cables, as well as your TV to use HDMI. This will bypass the SOC in the cable box. Here is some information on that converter: