The latest Microsoft Windows security updates have revoked a security certificate somewhere in the chain used to sign mumble.exe. This is causing mumble not to start up correctly.
A new version of mumble with a new security certificate has been released. All users of mumble should uninstall their current version (you can leave all settings files etc.) and install the fixed versions:
Mumble 1.2.4 experimental snapshots (local mirror)
I should add that in my experience you are fine running the snapshots; things rarely go wrong, and there are some speed improvements and bugfixes.
From the Mumble Blog.