If you say that one of your computers works fine when running the SlingPlayer software version, the issue is not related to the Slingbox but that specific computer. Otherwise, all of your computers would show the same behavior.
I recommend you to uninstall and reinstall the SlingPlayer software version and update the video drivers on this specific computer. Make sure to follow these recommendations and let us know how it works.
Thanks for the response, ranaleon. I un-/re-installed the desktop player, and checked for an update for the video driver (there wasn't any.) Same problem.
This has worked without trouble on this laptop in the past, although it had been many months since I used it (not my primary computer.) The only thing I can think of that changed is it was upgraded to Windows 7. My primary PC is a desktop that also uses Windows 7, and Slingplayer works fine on that, as it does on our other Win7 laptop.
Totally agree that the problem is local to this laptop. This is really strange...