Yeah, use something other than Lightroom to copy (not move) the files onto your computer so you can troubleshoot things. If you are not using a card reader, I'd get one to eliminate camera/computer comm issues. If you are using a card reader then try opening the card folder in your system browser so you can copy them over.
Alternatively you can try using EOS Utilities or ZoomBrowser to get the images off the camera, or ZoomBrowser to copy them off the card/reader.
If you are having problems opening up the card folder you may have a card problem or a cable problem. Realize also that viewing the image in-camera is not viewing the Raw file but only an embedded jpeg -- if the card is corrupt then the Raw data could be messed up even if you can see the jpeg.
Once you copy them onto your computer, a quick way of checking the integrity of the files is to open them in the Canon software -- ZoomBrowser will show you the embedded jpegs, but you need Digital Photo Professional to view the Raw files.
You can also import files into Lightroom from a folder on your hard drive using the Import from files/folders if you succeed in copying the onto the computer and viewing them in DPP.
If, though, any of these things fail to work, you may have a corrupted card. You can try one of the image recovery programs to run through the memory card and "rescue" the image -- they are pretty effective.
Well, give things a try!