The light is on because there is a problem with the emissions system. The engine may appear to be running fine but the emissions of the engine are out of spec. It may be as simple as a loose gas cap. Have the ECu scanned with a scan tool to retrieve the code that has been set by the ECU. This will help you find what part is being effected.
You need to start by having it checked for codes. Then you will know what to diagnose/fix.
check O2 sensor
sounds like a (tps) throttle position sensor. need to have it put on a scanner to check what trouble codes are stored in the ecm.
Check your pcv valve or your gas cap :P
Sounds like either your fuel pressure regulator, fuel filter or throttle position sensor.
and what code does the check engine light say ? go by autozone they will check it for free and get the code.
relay
Check engine light, low power, no start, runs rough, bent valves,Check engine light, low power, no start, runs rough, bent valves,
The a/c pump kicks on and off to compress the cold air. When it does this it draws power from the engine. The check engine light for misfire is probably from a different problem like timing or spark plugs
There are pages and pages of things that can cause a check engine light. You need to have it checked with a scantool. Then the code can be diagnosed and repaired.
If there aren't any problems with the operation of the vehicle replacing a censor isn't necessary . By disconnecting the battery terminals and reconnecting this will eliminate the engine light.
Auto Zone will check your engine codes for FREE. Then go from there.