The reduced engine power light is on in my 2005 Chevy Cobalt. In addition, it's sounds as though it's barely running. Any idea what it can be? The check engine light is on also, however I addressed this check engine light in March of this year, whereby an oxygen sensor was installed. I'm at a lost

The check engine light being on now is a different problem , Have DTC'S - diagnostic trouble codes checked ,will have something to do with electronic throttle control . That is what reduced engine power is about . It's in a reduced power mode.
Reduced Engine Power Mode
When the ECM detects a condition with the TAC system, the ECM may enter a reduced engine power mode. Reduced engine power may cause one or more of the following conditions:
• Acceleration limiting--The ECM will continue to use the accelerator pedal for throttle control; however, the vehicle acceleration is limited.
• Limited throttle mode--The ECM will continue to use the accelerator pedal for throttle control; however, the maximum throttle opening is limited.
• Throttle default mode--The ECM will turn off the throttle actuator motor and the throttle will return to the spring loaded default position.
• Forced idle mode--The ECM will perform the following actions:
- Limit engine speed to idle by positioning the throttle position, or by controlling the fuel and spark if the throttle is turned off.
- Ignore the accelerator pedal input.
• Engine shutdown mode--The ECM will disable fuel and de-energize the throttle actuator.

Do you know what electronic throttle control is ?
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Throttle Actuator Control (TAC) System Description

The throttle actuator control (TAC) system delivers improved throttle response and greater reliability and eliminates the need for mechanical cable. The TAC system performs the following functions:
• Accelerator pedal position sensing
• Throttle positioning to meet driver and engine demands
• Throttle position sensing
• Internal diagnostics
• Cruise control functions
• Manage TAC electrical power consumption
The TAC system includes the following components:
• The accelerator pedal position (APP) sensors
• The throttle body assembly
• The engine control module (ECM)

Your best bet , take it to a qualified repair shop .