You can delete all WP files from your server, as long as you leave the database untouched, nothing can go wrong. Like I said, it doesn’t hurt to make a database backup just to be sure, but such a backup does not include your WP installation. If you have more themes than the one you think causes trouble, I’m sure you have them on your computer? If not, you might want to copy the wp-content folder to your computer before deleting the rest. That’s the folder where themes and plugins are uploaded to. As for all the WP files that come with a download, you can just remove and replace them. Make sure to give the wp-config the same credentials as it has now, so the new WP can ‘talk’ with your old database. If everything works again with the default theme, you can reupload the new themes that you wanted to use, except (of course) the theme that you think caused the problem.