One of the most maddening problems you are likely to face with WordPress is when your widget admin stops working. Most times this is due to either an issue with your WordPress install itself or a permissions problem. So the first thing I usually try when I can’t open or move widgets in the admin view is to backup, erase everything but wp-config.php and manually reinstall WordPress. This will replace any corrupt files and will reset any permissions to what they should be and works 98% of the time for me.
But that other 2% can drive you crazy as I recently found out with my wine blog. Nothing worked and I was just about to start deleting database tables when I found a random forum post that, to my surprise, actually worked. All you need to do is install the ‘Use Google Libraries’ plugin and your broken widgets will work again. I suspect some sort of problem with script.aculo.us in my case but this plugin is also good for page loading speed so it’s a win, win!