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No, not possible, you can however reapply the last OS Update, but only if you have that one already downloaded manually to your Mac.

I know what your issue is, even if you could somehow reinstall 10.8, how the hell can you get connected again after doing so!

Oh, and I think the last poster in your linked thread has it right, after a restart it won't see any Monitor, so that might be the problem, there is no image/video output.
 
No, not possible, you can however reapply the last OS Update, but only if you have that one already downloaded manually to your Mac.

I know what your issue is, even if you could somehow reinstall 10.8, how the hell can you get connected again after doing so!

Oh, and I think the last poster in your linked thread has it right, after a restart it won't see any Monitor, so that might be the problem, there is no image/video output.

The Macmini has been restarted loads of times since it was set up, so I'm not sure this is correct. It also doesn't explain why VNC displays the login screen.
 
that's because osx starts up the services before it allows the user to login via the GUI, like any unix derivative

the answer is still no
 
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