All users get a login failed screen

Aside from moderated registration (which you mentioned you are not using), the only other thing I can think would fail all logins would be if you had some plugin that applies a third validation element to the WP login (such as a captcha). Most should be compatible with WP-Members, but that’s only if they are able to load their scripts on the front end. If not, then login would fail or a workaround would need to be factored into the WP authentication process.

Since you put a link to your site, I took a look at your /wp-login.php page, and you’ve got a popup captcha on there. I would suggest testing without whatever that is from as that might be the issue.