MiniDisplayPort to HDMI adapter not working
It could be the adapter?

I bought mine at Monoprice for $6.82!

Notice it says with Audio support in the title.


  Mini DisplayPort to HDMI® Adapter w/ Audio Support Product Number:
  5311


and it works purfectly on my MBA with the Sharp TV.

It is not worth for $4, but if you must, look in your about this mac, or your System Utility display if it shows the monitor/tv you just connected.