After upgrading Mac mini to Mountain Lion, the display is not working I had my Mac mini connected to a TV using VGA (with the mini DisplayPort-to-VGA adapter) running fine. After upgrading to Mountain Lion it simply doesn't work anymore.

I wasn't using any software like screen res or so, just pure OS X. Any tips to get that back?
Try logging into the machine with your display hooked up with HDMI (just so you can login), then switch over to VGA. Then try CMD + F2 (brightness up) to force detect displays and see if it switches over.