Breaks widgets

Could you try to log in to your site via FTP, delete the existing Jetpack folder, and reinstall the plugin manually?
http://codex.ww.wp.xz.cn/Managing_Plugins#Manual_Plugin_Installation

If you still experience issues, could you try to deactivate the Widget Visibility module, and see if you gain control of your widgets again?
You can follow the instructions here to learn how to deactivate a Jetpack module:
http://jetpack.me/support/#turn-off-jetpack-modules

Thanks!