There a few parts that go into the your Saturn's secondary air injection system. We'll start from the main component which produces the air that feeds into the exhaust manifold, and that being the electric motor (air pump) located towards the front passenger side of your Saturn's engine, next to the air conditioner compressor. Second is the diverter valve which is attached to the air pumps outlet. Third is the air injection systems control solenoid which triggers the diverter valve open or closed, and finally we have the air tube located between the diverter valve and the exhaust manifold.
The most common problem we find on Saturns is a plugged up air tube (the one located between the diverter valve and exhaust manifold). At times the exhaust manifold too will have carbon build up and require cleaning.
Start with ensuring the air pump motor is running. Start your Saturn's engine while it is cold and listen (or place hand on pump to feel for vibration) to the air pump. If you do not hear the motor running, the fault may be with the motor itself or the power connector to the motor. Disconnect the connection and check for voltage. If voltage exists, then you may suspect a defective air pump motor. Replace the motor and continue testing.
If the air pump does run, disconnect the tube going to the diverter valve and check for air flow. If no air flow, inspect the tube for obstruction. Usually the tube will be clear, and you should move on to checking the diverter valve's solenoid. The solenoid is located next to the diverter valve. It will have two vacuum lines. One leading from the intake manifold to the solenoid (vacuum supply), and one vacuum line leading to the diverter valve. While the engine is idling check for supply vacuum. Disconnect the vacuum hose first from the manifold side and check for vacuum, and next from the solenoid side. You should see approx. 18in of vacuum during idle. If no vacuum is present, inspect the vacuum line for cracks and/or disconnection. If no vacuum problem exists, move on to the diverter valve itself.
The diverter valve is located in front of the exhuats manifold (front of engine when standing in front of vehicle). It is an aluminum colored valve with an aluminum hose leading to the exhaust manifold and a rubber hose leading to the air pump. Disconnect the shorter aluminum tube leading to the exhaust manifold. More than likely you will find a large amount of carbon build up. Clean the tube out. Inspect the exhaust manifold as well. If it appears to be plugged up, you may need to remove the manifold and clean out the carbon.
Somewhere along the line of performing the steps outlined above you should find the fault causing your Saturn to trigger P0410. It is a common fault, and not too difficult to isolate and repair. After the repair(s), you'll need to reset your Saturn's computer in order to turn off the check engine light. you may also choose to not reset the computer and drive your Saturn for a few hundred miles over the course of several days... and the light should turn off by itself. If you choose to reset the computer manually (using a scan tool), your Saturn will need to complete a Drive Cycle in order to complete (make READY) emission readiness monitors. Driving your Saturn for a week, in both highway and city roads, will complete the drive cycle. So... either which way, once the repair(s) are made you will need to drive your Saturn until it is ready for a smog check retest.