You should be able to see the files on the card and just drag them over though - if the camera is connecting properly and being recognised.
I wonder if they haven't been recorded and finalised correctly, which could make them unreadable.
A possible reason for this is unsuitable card or card not formatted in the camera, from the menus when first put in. 

It would be worth trying a different card in case the one you have as failed or not fast enough.
For HD Video you nee a Class 10 card or it can't write fast enough.
This is another possible reason for failed recording. 

You can get a mini-SD reader or USB adapter and plug the card direct into computer rather than connect camera.
This is always my preferred way of downloading as it saves ferreting about for a lead.