Welcome to the answer forums. With the Tablet not connecting but the computer connecting I do not feel that the issue lies with the Slingbox. What I would suggest is unistalling and reinstalling the app on the tablet and seeing if this clears up the issue, With the Slingplayer already being install it should not charge you again and if it does you would want to contact the Google Play Store and they would be able to refund you the $14.99.
Hope this helps,
Sling Moderation Team