is ur PSU supposed to survive crank?
anyway, my old car-pc was using the Opus 150watt dc-dc PSU
it was great and would survive crank, then suddenly when i would start the car with the pc on, it would either freeze or reset.
i replaced my car battery with a bigger one (Optima Yellow Top D34) and the problem went away.
i was thinking, maybe when i started my car, the battery level would drop well below the threshold for the PSU to survive crank.
look into that! invest in a good battery if you replace yours.
edit: just realised you said you plugged your PSU into the ciggie lighter, is this the main source of power?
shouldn't you have a wire from your psu going straight to the battery? for constant +12v and another wire for the remote signal (to tell the PSU to turn on when you turn ur car on)
if you don't that could be another reason.