Why would the login page reload indefinitely?

I tried to log into a blog I administer, after 2+ weeks of no issues, and today I suddenly cannot log in. I have not updated the core or any plugins. The DB hasn’t changed, and no significant changes have been made to my system. The server admin has told me that nothing on their end has changed in the last 48 hours.

I’ve tried IE, Firefox, Chrome, Safari and Opera, clearing cookies before each, in normal and private browsing modes. I’ve tried renaming my plugins folder and my theme folder. It’s not a password issue. The login page just reloads over and over, and it just started happening out of the blue.

I’ve run into many posts about this, and disabling plugins or changing settings on config.php seem to be the most common solutions. But none of these have worked for me. While I cannot log in, the blog is online. I checked the source, and it says it is now 3.5.2, even though no one updated. I did a manual downgrade, which produced no error messages, and the problem persists. Any new suggestions?