when I try and copy the files over to the public directory, it doesn't work.
There are only three things that actually need to (and must) be copied to the site's new location:
1) database;
2) wp-config.php (matching that database);
3) the entire /wp-content/ folder with everything intact inside.
Two days ago, I managed to mess one of my sites up rather badly. I tried for a while to fix it, then just gave up on that and completely deleted *all* wp-whatever folders and files other than wp-config.php (file), wp-content (folder and its contents) and my .htaccess file. After doing that, I uploaded fresh copies of the deleted wp-folders and wp-files...and then logged right back in just as if nothing had ever happened. You can do essentially the same and have it all working in little time at all by just *first* dealing with some very specific needs in relation to wp-config.php.