My Xbox 360 Hard Drive isn't Reading that it is in the 360. What do?

I Turned Off my 360 and Un-Plugged my Hard Drive and brought it to my Friends House so we would have the DLC me and my Brother have bought and when I plugged my Hard Drive into his it didn't Read that my Profile my Brothers Profile or my Friends Profile were on there and when I tried to Recover my Account it said that there was not enough Memory or that the Hard Drive wasn't Plugged in. I have the 120 GB HDD version that is for the 360 Elite 2008 Edition so the most Recent Elite Generation seeing as they never made Updated Elites after 08. I am just hoping my Hard Drive isn't Broken because if it is and I go Home I am gonna have nothing to do seeing as that is how I Communicate with all of my Cousins. Is there anything I can do? Is there anything I can change or maybe do something differently when Plugging my Hard Drive in? Because I Plug the Hard Drive in Starting by Setting the Back in First then Plugging the Front in.