Have reviewed your installation and the issue was resolved after disabling the Joomla system plugin jfusion16_override. Please also confirm if working, please keep in mind you're on J1.7 and not J1.6, so likely that extension is going to fail. Please also confirm if is now working for you or not.

Please also note your install is out of date and highly recommend upgrading to J1.7.1 as it addresses some critical security issues.

Your site whether component related or hosting related appears to have redirects in place, which is what is causing your issues. For example trying to navigate to http or https version of /administrator sends me directly to your frontpage, which is not normal behavior.

If you have a .htaccess present please rename or delete it and see if this will resolve the redirects. Otherwise please using phpmyadmin or any other database management software and navigate to _extensions table and disable the Joomla system plugin Redirect. Once done reconfirm if still present as I can no longer reach your backend so can not test further. If still not resolved please contact your host to see if they have any redirects in place.

do I still need to log in to the phpmyadmin to disable the redirect plugin?

Nope.

We added the plugin for when users register so that they are directed to the login page with a message.

I see, this is likely causing you problems. Please disable usage of Redirect and install incubator project CB Auto Actions (released as of today) then configure a Redirect action using the after registration trigger. This will allow for a proper API redirect (supplying a message is supported).