Oh man, that's got to be a frustrating one. Can you remember back to when the issue first started happening? Was this when you first installed WP or did this eventually just 'happen' at some point when you were using WP?
Also, what browser are you using? Does changing browsers help any?
Are there any other WP-related problems you're experiencing or just the Sidebar issue alone?
Also, can you try deactivating your plugins and seeing if that helps any?
I have heard of some people having issues with their sidebar widgets freezing in similar manners because of plugin issues.
Deactivate your plugins one by one and try accessing your sidebar widgets again and seeing if that helps any.
If it does help, then your culprit is a plugin whose coding somehow interferes with the sidebar. If not, it still might be a plugin problem in which case: if possible, make a backup of your non-WP-bundled plugins and after deactivating them all, delete them all and then reload your WP admin panel and see if that clears out the problem.
I hope the resolution comes swiftly!