Ok, I think it is clear what has happened, and it is easy enough to fix. Also, to clarify, WordPress is installed in your “home” or “base” directory (yourdomain.tld). The wp-admin, and other directories are part of WordPress, and they normally reside a directory level below the main WordPress installation.
Using the control panel overwrote your existing .htaccess (the one in which WordPress had its Apache re-write rules) with the one you presented in your post.
What needed to happen, was for it to add the authentication stuff to the existing file. Stuff like this (and pangea33’s observation about the location of your .htpasswd file) is why many elect to construct their own authentication lines in the .htaccess file, rather than letting the Control Panel do it for you.
That said, here is how I recommend you proceed:
download a copy of your existing .htaccess file (the one you included in your post, and rename it to something on your computer.
Use the Dreamhost “automated backup” .snapshot directory to find a copy of the .htaccess files that worked properly for your WordPress installation before you password protected the directory, and download it to your computer.
Combine the contents of these two files into one new .htaccess file, with the contents of the file in step 1 inserted into the file before the contents of the file in step 2 (use a text editor - either retype or cut’n’paste)
Upload this “new” combined .htaccess file to your home directory, overwriting the one that is there now.
Clear you browser’s cache, and test.
note: Of course, if you are comfortable editing from the shell, you can do all of this there - just combine the contents of the two files into a single .htaccess file, with the respective contents in the described order.
If you did it correctly, you are done! The new .htaccess file will provide the password protection you want, and your Apache re-write rules will have been restored so that your permalinks will now work. Good Luck!