2003 Galant service eng light comes on, show random misfire. replaces plugs, wires, dist cap. did not solve issue. ck eng light keeps coming on. what is the next step?

Check for a shorted spark plug ie. touching central and side electrodes.

It could be a bad plug wire. Swap the wires with another cylinder and see if the misfire also moves with the wire. Or a bad Coil/Dist Cap.

have you checked timing ? can be injectors bad or in fuel system . i think it could be a injector bad.

Sounds like either a bad plug or wire, replace both.

is it misfiring ? if not reset see if comes back

Could possibly be the coil pack has a crack in it, could also be plug wires have cracks in them as well, sounds like time for a tune up. Recommend replacing plugs and wires, and if that doesn't solve the issue then spring for the coil pack. Scanning the computer will tell you what code you have to help point you in the right direction as well. If you have any p0300-p0306 codes those are all misfire codes.p0300 is random multiple misfire, p0301-p0306 are individual cylinder misfires.

DTC code P0421 is the O2 sensor that indicates a an issue with the Catalytic Converter. Replace the O2 sensor to the Catalytic Converter "the one after Converter" It's common for the sensor to fail and you can pick one up from Auto Zone and they will have the step by step instructions to replacing the O2 sensor. 
DTC code P0302 Indicates a misfire on cylinder #2. Address the spark plug, spark plug wire, and injector. Look for any damages and try running some fuel injector cleaner through the fuel system to clean out the injectors. 
Good luck and hope this helps. 

When the water pump leaks, it leaks right onto the Opti-Spark distributor. It will cause the same issues you are having. Replace the Opti along with the spark plus and wires.

it is your fuel injectors, replace them, and the problem will be solved..

Is this a 5.7? They are notorious for intake manifold gasket leaks. When mine did it, the diagnostics blamed it on an ignition misfire also! Replaced the gaskets and it runs smooth!