Sputtering and hesitation when started

You mean it "won't"? Test fuel pressure while cranking. Test for weak spark.

Possible water pump. Remove the belt and grab the pulley , wiggle and spin. Check the other pulleys as well.

This is likely a problem with the Mass Airflow sensor, it is a sensor that reads the amount of air going into the engine, when it fails it causes severs hesitation and power loss. Contact a local parts store or your GM dealer for a rebuilt one, the part is about $150.00. It is locate in the air intake hose to the engine.

you have to monitor the fuel pressure, if you find that the pressure drops off as soon as the engine has started you should check the fuel pump resistor located on the frame next to the windshield washer tank. If the resistor is ok see if you can keep the engine running with carb cleaner. If the engine stays running on the carb cleaner try disconnecting the mass air flow sensor and see if the engine continues to run by itself. This is all taking for granted that there is not a security system problem. check if the security light keeps flashing while trying to start.

The TDM in the security system (VATS/PassKey) is having problems, it's typical on those cars and it will get worse till the car wont start anymore. You can find a great write-up here: http://newrockies.ca , it was the only thing that saved my Park Avenue.

this also happened to me. anyone ever fix this or know the reason?

It could be the park safety that works off of your brake switch , may need to be replaced , it is under the dash hooks to brake lever, don't know if you can adjust it or just hook it back up try holding more pressure on brake , please let us know what happens , Thank You .

check the idle air control valve, it could be damaged or dirty

Per your description, it sounds as though you have a stuck injector. I assume you have a service engine light on. Take the vehicle to your local Auto Zone or Advance Auto Parts and ask them to scan the car for trouble codes, they will scan the vehicle at no charge to you.
Write the codes down and respond back to this post and we can get started.
Let me know.
Regards,

Had the same problem drove me nuts until I tried disconnecting Mass Air Flow Sensor, the car should drive normally but with a "Service Engine Soon Light" on. Mass air flow can run from $140 up, picked one up at recycler for $40.

Worth a try.