Your Saturn SL2's Air Injection Pump will run on startup when your Saturn's engine is cold using data from the coolant temperature sensor. The colder the coolant the longer the air pump will run. The air pump is used to inject oxygen in to the catalytic converter promoting the burning of the fuel mixture when the engine is cold. The AIR pump receives power from the air pump relay, which is controlled by your Saturn's PCM.
An important component to inspect is the AIR injection vacuum valve which is controlled by the air injection solenoid. When your Saturn is cold go ahead and disconnect the vacuum line going to the air injection valve and check for vacuum. If you have vacuum, using a hand vacuum pump, try opening the AIR injection valve manually. The valve should open and direct air to the exhaust manifold.
Trouble Code P0410 is typically caused by a defective AIR injection vacuum valve or AIR injection vacuum lines. The valve and thin vacuum hose are vulnerable to high heat.