Hey there, Yolanda_22.
Do you hear the drive spinning or can you feel it vibrate? I'm asking because if the drive does not spin up then there's not much you can do. Give it a try with a different computer and a different USB cable to see if the same thing happens.
For data recovery (only if the drive is spinning) you could give it a go with Ubuntu Live USB/DVD, to see if that OS is capable of properly recognizing the HDD's partition/s and if you can get to your files. Other than that perhaps data recovery software might do the job: http://pcsupport.about.com/od/filerecovery/tp/free-file-recovery-programs.htm. Basically your most reliable option would be a data recovery company, so you could get in touch with the drive manufacturer's...