There is no need toremove the water pump for a complete system flush. Both knock sensors should be removed to get the old coolant out of the block. It can be a messy job but not a tough one. With the car being 12 years old, yo should replace the upper and lower radiator hoses and the TB hose. The heater hoses are pretty pricey but if they look to be in good shape, just leave them in.
Remove the pressure cap at the expansion tank.
Drain the radiator at the petcock.
Open the bleed valves on the thermostat housing and on the throttle body (driver's side at the lower side of the housing).
Remove both knock sensors. (think you need a 21mm socket)
Close the radiator petcock and fill with water until water runs out from the block flushing all the gunk in the block. Re-open the petcock and drain radiator.
Remove the overflow tank and clean out. Do not re-install yet.
Re-install the knock sensors and close radiator drain plug. Fill with water until water begins to flow steadily from the bleed valves (Be careful to not let water flow down to the bottom front of the motor where the Opti-spark distributor is. Get this soaked and you can figure on $400-600 to replace :eek )
Close bleed valves and fill expansion tank.
Start the motor and run to almost operating temp watching the digital coolant display. Shut off motor and let cool.
Repeat the above until clean water drains out.
When you replace the knock sensors for the final time, use a light coat of anti-sieze compound on the threads. Don't use teflon tape as the sensor body has to ground to the block. Tighten to about 15 ft-lbs.
Reinstall the overflow tank but leave it empty. With radiator drain closed and bleed valves open, add 2 gallons of ethlyene glycol (green) coolant. Then finish filling with distilled water (per sevice manual and only costs about a buck a gallon at a grocery store). you will need about 3 gallons. You may also want to do the final flush with distilled water to get any minerals in tap water out. That may take 4 gallons more.
When the coolant comes out of the bleed valves, shut them and fill the expansion tank about halfway. Start the motor and watch for a drop in the coolant level in the expansion tank when the thermostat opens. With the engine at about 1100RPM, fill the tank to just below the lip of the opening and install the cap.
Check for leaks around the hoses if you replaced them (I re-used the factory spring clamps. They have the correct tension and they're free! If the water temp shows overheating, shut down the motor and let cool. Remove the pressure cap and check coolant level. Open the bleed valves and make sure you get a steady stream of coolant out. These valves help remove air pockets in the system.
Add a 50-50 mix of coolant and distilled water to the overflow tank to the Cold mark if the motor is cold or to the Hot mark if engine is warm.
One of the biggest problems with cooling in C4's is debris and dirt getting caught in the A/C condensor and radiator. Look up under the front plate to look for stuff there. You can use a stream of water from a garden hose to push junk out from the back side of the radiator by aiming through the fan housing.