I upgraded to WordPress 3.5.2 a couple of days ago when it appeared on the dashboard and then went back to whatever I was doing. Yesterday, I tried to connect to the admin dashboard and was unsuccessful. No login box, just an eventual timeout. I had similar results when I tried using the WordPress app on both my iPhone and my iPad.
I’ve experienced this a couple of times in the past after an upgrade and it often seemed to be solved by disabling, and sometimes uninstalling, a plugin. After a little experimentation, I have come to the conclusion that it seems there’s something about the combination of WordPress 3.5.2 and WP Super Cache that causes problems. When I removed the WP Super Cache plugin, everything started working again. Reinstalling it caused the problem to return.
I like the WP Super Cache plugin, so hopefully whatever the problem is will be resolved by the programmer so that I can reinstall it.