I used Skype to connect Touchpad to a laptop this week with audio and video, and tonight from Touchpad to Samsung TV (audio only because I need to buy a camera for the TV tomorrow).
Are you able to have the Touchpad at least "dial" the Skype account to establish an audio call?
I just ran a test where I made my TV "invisible" status. The Touchpad shows that account in the Phone Dialer/Contacts screen as "(Offline)". I pressed on it on the Touchpad and it dialed it just fine and the TV allowed me to answer.
I ran another test where I logged out of Skype on the TV. The Touchpad shows the TV as "(Offline)". I pressed on it on the Touchpad and it dialed the TV just fine. However, the TV didn't show a "incoming call popup" because the Skype app isn't running.
Another setting you should check is in the Phone app, go to the Preferences&Accounts screen. There is a "Calls" setting where you control what the default mode is when the Touchpad has both a Skype and a phone connected to it. I have that set to "Always Ask". This probably isn't your issue, but wanted to mention this setting just in case there's some quirky bug somewhere.
Anyway, see if you can do some kind of similar tests to see if you can get something similar (or not) and report back. In all of my tests, as long as my contact in the Touchpad had a Skype account, I could "dial" them from the Touchpad regardless of their status.