When you plug your camera in...is your computer recognizing the camera? If it is being recognized by the computer, does Lightroom bring up any error dialog boxes when you try to use it? I also have the 600D, so I am going to try it myself and see if I can help you anymore.
According to this docuemnt, "Shooting in Lightroom" is not yet supported for the 600D http://helpx.adobe.com/lightroom/kb/tethered-camera-support-lightroom- 4.html
While Raw files are currently supported, tethering is not yet. The earliest it can come, if at all, is the next Lightroom "dot" release which happens 3-4 times a year. The last one was May 29th.