Menu can't be opened/closed

If you are sure, that it’s not a configuration issue, in the Advanced Parameters, the Opened isn’t selected incorrectly, and at the Always opened levels, there isn’t any selected (you can deselect by pushing Ctrl button, and click), then it will be either the previous problem, or a javascript error. The best javascript error reporter is in Firebug, so install it on your Firefox browser, press F12, click on Console, and refresh the page, where your bad menu is. It will write out some javascript error, which will probably give you a hint, which plugin/extension is causing it.