Apple - Rebooting a headless Mac Mini
Older Mac Minis don't like running headless (without a monitor)
Here's one solution involving some cunning use of a display adaptor and a 100 Ohm resistor.
You don't need a DVI to VGA adapter. Just plug the resistor between C2 and C5 holes on the DVI. (Any of C1, C2 or C3 should work, but I tried C2 and C5 first and it worked for me so I stopped right there.)
The resistor should be about 80 Ohm, but the closest I had was 150 Ohm resistors and that worked fine. 200 or even higher probably works too.