When I bought my Mini to act as an in-house server, I thought I somehow broke it... it installed fine, but as soon as I removed the keyboard and monitor and moved to a quiet corner that was to be it's home - it suddenly stopped wanting to boot. Google is my friend! It turns out that Minis don't like to run headless, so it requires some fancy footwork to get things running. I used the DVI to VGA adapter that came with the Mini, a 100 Ohm resistor (70-80 Ohm would be best), and a pair of pliers.
Why it works: VGA standard looks for a signal on green to detect whether or not a monitor is attached. The resistor provides enough termination on the green and it's ground to trick it into thinking there is a monitor present.
Follow along...