Thanks for providing the extra information Anastasia.
There is a possibility that one (or more) of the clips on your Sony camera is corrupted. Winston has mentioned a possible corrupt AVCHD file structure, but it may be a problem with just a single clip - see this post by mannyme here:
http://discussions.apple.com/thread.jspa?threadID=2027751
The post by mannyme refers to a SDHC card, but the same principal would apply to a hard drive camera.
By the way Anastasia, what model is your Sony? Could you let us know please.
Given that things have worked for you previously, like Winston, I'm thinking that the problem will be with the camera files. So, as mentioned, look at all clips on the camera to identify if any do not play. Look for any black clips with a question mark (as discussed by mannyme). If you find any problem clips, delete them - then try the import process again. Connect the camera, _with iMovie open_, and once identified (hopefully) use the option File>Import from Camera.
Hope this helps Anastasia! If not, there are other things we may be able to try, so don't give up yet!
John