What does media test failed check cable mean?

It depends what context...

I think you are talking about when a computer is starting up (pressing the power-button)

That means one of two things.

Linux

1) The hard drive where your Operating System (Windows XP, Windows Vista, Linux, MAC OS X) is not present, or not properly connected to your computer.

2) If the hard drive is successfully connected, there is not an Operating System Installed on that hard drive, and thus it will not start your Operating System

Either way, I think this message is preventing the startup of the Operating System.