OK--figured it out on my own. First, there are TONS of complaints about slingplayer not connecting. You would think that SLING would put a team on this issue and develop an app that WORKS. Instead, SLING uses US, the paying consumer, as their testing ground. Very poor business plan there SLING.
For anyone looking for a possible cure, here is what I did. Sling does not offer a REINSTALL of slingplayer for the tablet, only the phone. So--on my tablet I opened the options menu and told it to discard all settings. That forced the app to re-initialize. Back working again, for now!