Question: My bluetooth mouse batteries died, and when I replaced them, the mouse didn't reconnect. Now how can I get OS X to discover and connect my mouse without having a mouse to open the mouse dialogue?

Answer: 
You can open the Mouse System Preferences by using Spotlight search. 

1. Press `⌘-Space` to open Spotlight. Type "mouse" to find the Mouse System Preferences and press `Enter`.
2. When the Mouse Preferences are opened, make sure the mouse is on and wait for it to be discovered. The "Connect" button should be blue, so you can press `Enter` to connect to it, and you're done.
If the batteries run out in my wireless mouse it never reconnects automatically and I have resorted to reconnecting a wired mouse to click on the bluetooth icon in the menu bar. Then I found that you can activate the bluetooth icon by pressing Control-F8 (the "Move focus to status menus" in the keyboard shortcuts) and using the cursor keys and the enter key to get to the connect menu item for the mouse.