What version of Lightroom?
In LR3 (on PC):-
1. at the middle top of the import screen are 4 options "Copy as DNG", "Move", "Copy", "Add". Which of these is highlighted? If not "Add" then change to "Add" and try import again. Also see 3. below
2. near the top right-hand side is a checkbox "Make second copy to:" Is this checked? If so look at the folder name shown below it and check it exists and has sufficient free space (a few Gb at least) and you have write permission to it.
3. If import method (in 1. above) is not "Add", have a look under the "Destination" pane on lower right and check that the highlighted folder exists (it should) and there is sufficient free space and that you have write permission.
If none of the above then I'm stumped
...
Cheers.
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Just saw this...Hmmm that pretty much means what I wrote above is probably not relevant.