It sounds like you have your import process set to Add the files to your catalog from where they are instead of to Copy the files to the hard drive and then add them to the catalog.
Look at the top of your Import dialog and see which option is selected.
Oh, you're right! Do I need to re-import those files now in order to store them on my hard drive?
They are already in your LR catalog so there's no need to import them again. If it were me, I would put the cards in one-by-one and and use the Folder Panel in Lightroom to drag the files onto your hard drive in a location you desire. As long as you drag the images around inside of Lightroom they won't get lost. (Which can happen if you us the OS to do your moving) You can then import new photos to a similar location as you shoot more pictures.
It's not possible to import the photos into Lr using the 'Add' option or even the 'Move' option. Both are greyed out in 'Import' window. Given the OP's description I would hazard a guess that the files haven't been imported at all. Instead the OP is viewing them in the Import window.
The OP is on LR 4 which, If my memory isn't faulty, used to allow you to spoof a drive by selecting the memory card in the Files section instead of the Devices section. I can't remember which dot release fixed that (it may have even been LR 3.x)
That does not make what you say "untrue". The OP will have to let us know if the imports were completed or not.
You're right, both options are greyed out. Why is this the case and how can I fix it?
Move and Add are normally disabled for non-hard drive removable media. This is to prevent people from losing photos and all the work they might have done on those photos.
Normal Procedure is to:
1. Insert your camera's media
2. Import into Lightroom using Copy which will make a duplicate of your file from your media and store it on your hard drive (or external hard drive - which ever you specify)
3. Remove media
4. Work on your images in Lightroom from the location they were copied to - never from the original media