Mac mini (Mid 2011): Plugging a device in the Mini DisplayPort during startup produces no video
Symptoms
You may notice that if you plug video devices into your Mini DisplayPort while your Mac is starting up, the computer starts up to a black screen. This issue may also occur if you plug in the Mini DisplayPort cable immediately after you hear the startup chime.
Products Affected
Mac mini Server (Mid 2011), Mac mini (Mid 2011)
Resolution
Make sure the Mini DisplayPort cable is plugged in before you start up the Mac, or wait until your Mac completes its startup and then insert the cable.
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Read more http://support.apple.com/kb/TS3979