When you import the Images from the SD card you also define the destination for the Images, its either the hard drive or external drive and I hope you aware that Lightroom only import the Smart previews for the images in Lightroom catalog.
if you check the Import window you have two major windows Source & Destination, Source is your SD card and Destination is hard drive.
Refer the below link for more information.
Hope that helps.
When you do the Import, you must select the COPY option, and under Destination on the right hand side, you must select a location on one of your hard disks.
Thanks so much for your quick responses. Yes, you are right... for some reason, I had "ADD" rather than "COPY" which is where the problem was. They are importing right now and I'm so relieved. Thanks again to you both for coming back to me.