2008 corolla s is having rough idle and loosing power. no check engine light

It could be many things, unfortunately and without hearing the noise first hand or being able to do some basic diagnostic tests or be able to drive the car, its hard to say what the source of the noise may be. Is there a Check Engine Light/Service Engine Soon light on? If so a scan tool will be needed to retrieve codes stored in the computer of your car. The codes stored in the computer would indicate where the problem is or even looking at the engine sensor data with the engine running with a professional grade scan tool may show what is at fault. If its got higher mileage the airflow meter or fuel pump or fuel delivery may at fault. Start with the basics have the spark plugs and air filter been changed recently?