2002 galant no start whining noise from starter

Is the engine turning over with the key in the start position? If the engine is not spinning over and you hear a whining noise, the starter is not engaging the flywheel. If the engine is turning over with the starter engaged, the engine has most likely jumped time that creates low or no compression which results in the whining noise.

Look more closely at the 1 and 4 coil, also, check for trigger signal to these coils. I mostly suspect the trigger unit.

you have to check spark from the plug....step1 pull out one of the plug wire step2 put one spark plug into the plug wire. step3- clip the plug body with jumper cable and the other to the negative(-)terminal step4 start the car and see if there is strong spark on the tip of the plug

Its common for this to happen if you have high millage, change the coil packs that should fix the problem

ignition controller (computer) - easy to check. hook up one or two of the old coils with old spark plugs. make sure plugs are touching metal on the motor (for grounding), have someone crank starter while you CAREFULLY observe plugs, you should see spark at plugs. if spart, i'd check for timing sensor problems, if no spark then problem is in ignition computer.

Yes your 4 cyl engine uses direct spark with a coil over each spark plug.
And the computer controls the firing of the plugs and injector pulse.
The problem could be the crank or cam sensor, or the wiring harness, but in most cases the check engine light should be on and a code set.
You might want to check the computer for codes, then try the cam sensor.

There is no simple answer, there are to many variables. If you have access to a scan tool, pulling the codes should help. Without them its back to old school hunt and peck method. At this point we need to narrow down the problem. You need to test for spark.

1. Tag and disconnect the spark plug wires from the spark plugs.
   
2. Remove the spark plugs and install the spark plug wires to each spark plug.
   
3. Ground (do not hold spark plug) the spark plug; check if spark occurs while engine is being cranked.
   

Crank the engine for no more than 2 seconds at a time to prevent flooding the engine with gasoline.
If you have spark, You will want to make sure you have fuel injector pulse, along with fuel pressure. If you have spark ..simply spray some starting fluid in through the air filter and hold the gas pedal to the floor and crank it over while spraying. If it fires up, you know it is fuel related( fuel pump, regulator, or ECM if no injector pulse) . If you have no spark then look at ignition coil connection and trace through to the distributor( if equipped ). The crank shaft sensor has a tendency to fail on these as well. This should give you a few things to test and check to start you on your way to narrowing it down. If you have no spark then look at ignition coil connection for power and trace through to the distributor( if equipped ). If it is DIS( no distributor). It may be the Crank sensor or the ECU. The crank shaft sensor has a tendency to fail on these as well.
The ECU uses the signal sent from the Crank sensor to trigger the spark and fuel injectors. ( make certain you have checked all fuses)

2 things that you have to check on no starts every time. Spark at spark plug and fuel. Turn key to run position and listen at gas tank for fuel pump to run you should hear a whining noise. This will only happen for 3 to 4 seconds then it will shut off until engine starts. You can turn key off then to run every 3 to 4 to listen for fuel pump. You may hear the relay click off in engine area even if pump does not run. Fuel pump failure is pretty common. If pump is running pull spark plug out or put a spare plug into spark plug wire and have someone crank engine set plug on engine and watch for spark. This will give you a starting point. Hope it helps.

check for a ground wire left off if it is not a starter prblem if so check wires on starter and battery ground to eng.

Check if battery is charging, could be a number of things. Alternator, Start motor or just loose wire somewhere in Engine bay!