I tried to open SQL Server Configuration Manager one day and got a sad face error dialog:
A quick search on google returned a few positive results. One of them looked especially promising: http://methmal132.wordpress.com/2013/10/04/how-to-resolve-the-sql-error-cannot-connect-to-wmi-provider
The blog post is a replicate of the knowledge base article: http://support.microsoft.com/kb/956013 but with pretty pictures.
If you are here because you had the same issue then you can stop reading if the above workaround resolved your issue. Unfortunately for me, I had compounded issues. It turned out my WMI was corrupt and I had to fix that first.
Off to google again and luckily I found this post: http://katyscode.wordpress.com/2007/02/03/tutorial-how-to-fix-wmi-corruption
Impressed with the level of technical details contained in the post, I religiously followed the instructions to rebuild the WMI repository word to word.
Once the WMI woes were sorted, I returned to the KB article for the workaround and that fixed my issue eventually!