Hello! I'm having, what sounds like, the same issue. Everything was working fine, until I ran a combined update, as prompted, for 10.8.2. After the normal reboot, the computer boots to a plain, white screen with no Apple. The computer is not responding to any keyboard command at startup, be it any of the reset commands, 'C' to boot to the optical drive, or option to select the startup destination. When pressing the Caps/Num lock keys, I notice that none of the LED lights will turn on on the keyboard. The piggybacked optical mouse is not showing it's red light from the bottom either. These tested fine on my MacBook Pro, however, and have always worked with the Mac Mini. Connecting and reconnecting the devices does not help. I know how to run all of the hard disk repairs, the permission fixes, etc., but it appears as though something is stopping my USB devices from being utilized (or even powered) at startup. I work in IT, and I support Apple computers every day (point being, I do know my stuff).
I opened the case and disconnected the hard drive from the logic board, thinking a potential hard disk issue is to blame. Upon restart, I still get the BONG (chime), but the machine will still not respond to any keyboard commands. Plugging in a USB stick that was created as a Mountain Lion boot device in Disk Utility with the InstallESD.dmg doesn't yield any results (as I am unable to 'tell' the computer to boot from it). The system disc that was packaged with the Mini is in the optical drive, but the Mini won't boot to that either. I'm at a complete loss. This is a 2010 model which was purchased new in December in that year. I'm using HDMI directly to an HDTV. The cable is working, the TV is working, the optical drive works in another machine, and the hard disc makes the necessary sounds (but not anything out of the ordinary).
To reiterate, this happened IMMEDIATELY after installing the combined 10.8.2 update. I am seeing a lot of posts about this issue, but no actual solutions. The dialogue seems to die somewhere after, "Reset the PRAM."
PLEASE ADVISE