When you imported the backup to your localhost, did you remember to change the stuff in the SQL file to reflect your localhost settings? Or did you just backup the live site and the import to your localhost machine?
Most likely, your database settings (and perhaps even your table prefix) on your localhost isn't he same as your live host. When you do this kind of thing, you have to open up the SQL file in a text editor, and change the database settings to reflect the proper database. If you don't do that, then what you're seeing will generally happen.
At this point, what I would do is drop the database from your localhost (and get that back) and then open up our SQL file and make the necessary changes (usually, it's just a matter of changing a couple of lines at the top of the file, so it points to the right database, as well as changing the wp_options area to reflect the correct home URL and site URL). Also make sure your wp_config.php file has the connection settings to your localhost machine, and not your live site. Save (and "Save As" - don't overwrite your backup) and import *that*.