There are several reasons you can get the Access denied error. Some files will NOT copy if they are in use like database files and outlook pst’s. More often than not the issue is security and you are being hit with a quota or inability to copy certain file types. Where are you trying to copy the files to?
Are you an Administrator on the box you are trying to copy to? What file types are being blocked? If you post some more info we will get this fixed up for you ASAP!
As for checking the security permissions of the target folder right click the folder and choose properties and then security you will see all the security information there.