Dictation has stopped working

Do a backup, using either Time Machine or a cloning program, to ensure files/data can be recovered. Two backups are better than one.

Try setting up another admin user account to see if the same problem continues. If Back-to-My Mac is selected in System Preferences, the Guest account will not work. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later.

Isolating an issue by using another user account

If the problem is still there, try booting into the Safe Mode using your normal account. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer. For each disable/delete, you will need to restart if you don't do them all at once.

Safe Mode

Safe Mode - Mavericks

New admin account - go to System Preferences under the  menu. When it opens, go the Users & Groups. Unlock the padlock by clicking on it. Then hit the + sign. In the new screen, in New Account, select administrator. Fill out the other details as desired. Quit System Preferences and reboot. Sign in as the user you just created. Test to see if Dictation is working there. If not, it is a system wide problem and not your user account.

Safe Mode - Shut down the computer and wait 10 seconds before restarting. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. See if Dictation works there. After testing, reboot normally.

Try running this program and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor. Please use copy and paste as screen shots can be hard to read. This will show what is running on your computer. No personal information is shown.

Etrecheck – System Information