The problem is not where you’re trying to import FROM it is where you’re trying to import TO – the destination. What is the destination you’ve specified in the Import panel? What permissions are there for your user on the destination folder you’re importing INTO.
The message you’re getting means that LR cannot READ from the files that it has just tried to Import to verify they are there—the files are not making it to the destination, not that LR cannot READ from the files on the card, which it apparently can because you’re seeing previews, right?
Are you on a Mac or PC?