What happens is Slingbox tells me to install Sling Player. ...... But SlingBox still refuses to recognize the installation and tells me to install Sling Player.............
I tihnk we have a terminology problem here. Slingbox is that lump of plastic you have sitting by your TV, it can't tell you anything. All the interaction is through some sort of viewing software, normally called Slingplayer.
Can you explain in a bit more detail what you see on the tablet when you tap on the Slingplayer icon ?