I have a 2003 Saturn Vue w/3.0l engine. Had a coolant leak at the head gaskets. Had the heads checked for straight and cracks. Replaced the timing belt and water pump. Now while running I have a flashing check engine light, codes p0300,0301,0303,0305. replaced the coil, checked the timing marks 3 times, all is ok. Will pop through the intake on accel.

SOURCE: car won't start

Only a few basic things are necessary for the engine operation 1. Fuel (To be exact proper air/fuel ratio, normally it is about 14/1)
2. Spark (in appropriate moment)
3. Proper timing (the valves should open and close only in appropriate time)
4. Compression in the cylinders (Normal compression is 120 - 170 psi. The engine won't start if the compression is lower than 70 - 80 psi.)
Plus, to start the engine, the battery, the starter and the starter circuit should be OK.

If the engine won't start - there's no magic - one of these things is probably missing. Most often it's a spark- or fuel- related problem, but often it could be very simple things like dead battery.
If the car won't start, check simple things first:
Make sure you have a fuel in the tank, oil in the engine and the battery is OK, follow this link - How to check the battery
Now simply answer the questions, press "Yes" or "No" (If it's blue, follow the link).

- Do you hear the cranking sound when you're trying to start your car? (Yes No )
- When you switch the ignition ON before starting a car, does the "check engine" light come ON? (Yes No )
- When you switch the ignition ON, do you hear fuel pump buzzing sound from the gas tank area? (Yes No )
Before your engine died, did you experience any prior events such as:
- leaving the lights ON overnight (Yes No)
- driving through a deep puddle, or washing the engine compartment? (Yes No)
- trying a jump start? (Yes No)
- having only a little fuel in a tank? (Yes No)
- having had the engine repaired recently? (Yes No)
- the engine was overheated? (Yes No)
- extremely low oil pressure? (Yes No)
- unusual noises such as knocking, pinging, whistling? (Yes No)
- smoking from exhaust pipe? (Yes No)
- strong smell of a gas? (Yes No)

Now, let's try again. Turn off the radio, try to crank the engine one more time, and listen carefully. Is the cranking sounds different than it used to be? If it's different, does it looks like the engine being cranked by the starter too slowly? (Yes No)
Is the engine being cranked too fast? (Yes No)

Hope this may help;

DON'T FORGET TO RATE::

SOURCE: 2003 saturn vue 3.0 engine, replaced timing belt,

You could have a leaking water pump gasket. Did you put sealant on it when you replaced it? were ALL surfaces totally clean?