This is a strange one... MOSS Enterprise publishing site, no customization of any kind and suddenly in both IE8 and IE9 I can no longer drag and drop web parts on any web part page. If I drag and drop a web part the UI responds and drops the web part in the correct location but then all of the SharePoint page editing controls become unresponsive.
For example, drag the first web part in the Middle column on a blank web part page below the second web part. The web part appears to have moved, I can invoke the edit block for the web part but if I select "Modify shared", Delete or anything else I get no response, nor do I get a response from the Save and Stop Editing button.
Happens on all of my sites including a brand new site collection, and it's local to my machine. Doesn't occur on another user's machine under my account or theirs. Googled myself half to death already, nothing relevant. Anybody?