To my knowledge the cobalt should run without oil, or oil pressure. I have bought them with broken oil pans and they start right up. You might have another problem. When you say won't start, do you mean won't crank, or cranks but won't start?
Cobalts may not start if...
ALTENTOR is bad or unplugged(this is because of electric power steering)
MASS AIR FLOW SENSOR is unplugged, or off, broken, vacuum leak
ANY PART of the AIR CLEANER ASSEMBLY is off AFTER the MASS AIR SENSOR
U1000 CODES, if there is a lack of communication between the modules(ABS too)
SECURITY LIGHT IS ON
TRANSMISSION not in PARK OR NEUTRAL, BROKEN SAFETY SWITCH ON CLUTCH PEDAL
OUT OF GAS
When you say you hit a rock, is it possible that you damaged the FUEL TANK, PUMP inside the tank, or Gas lines running under car to the engine. Maybe you hit so hard that you knocked a relay or fuse loose in the UNDER HOOD FUSE BOX. There is also a known problem of the GROUND WIRES mounted on transmission, close to starter, to the right of the starter, there's two sets on bell housing bolts. These grounds are known to corrode and break off or even look fine but with no connection, one of the grounds runs back the ignition module(engine will crank but not fire). These are things that I can think of, worth checking.
---------- Post added at 07:02 PM ---------- Previous post was at 06:56 PM ----------
Another note: I have used WINDSHIELD URTHANE and DUCK TAPE to fill holes in the pans to safely drive them around. And the oil pans are pretty easy to change and shouldn't cost more then say $50 from a recycler. If your near Grand Haven, Michigan. I have one here, on the shelf.....