Q: is it possible for apple device to just break down?  I can't get device to work, keeps blinking.  Tried unplugging and plugging back in.   Still won't connect to TV

Yes, it's possible that anything stops working at some point. Here is the support start page - you can read through the stuff and/or contact support:

http://www.apple.com/support/appletv/

If yours is no longer covered by a warranty, you can also take it to your nearest Genius Bar for a free evaluation.

given enough time everything breaks down

some things breaks down sooner that is the main cause of the warranty system

Try a restore.

Restore your Apple TV (2nd and 3rd generation) - Apple Support

 

Screen shows disconnected line to I-tunes icon.  

It is telling you it needs to be connected to a computer that has iTunes on it via a USB cable and have its software reloaded from iTunes.   Try that.  If it loads the firmware again you are good togo.  If it is not able to load the firmware it is pretty much dead.

With a mini USB, hook your Apple TV unit to your computer, and plug in its power cord.  Select ITunes on your computer, and after a few minutes it will recognize your Apple TV unit and at that time you can select RESTORE. Takes about ten minutes and will tell you when restore is complete and to return it to your TV and hook it up.