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Is the check engine light on? Need more info. What does it do in idle at lights? Describe the noise and when it occurs. If the check engine light is on, go get a free read at an autozone and post result.
Try this solution first, it may take care of all three codes for you and is a common issue on the G6 : http://www.g6ownersclub.com/forum/showthread.php?t=12532 The skipping might be the misfire caused by the faulty solenoids. Otherwise, the cat. converter may be fouling and throwing all the codes.
What do these codes mean, p0420, p0013, p0010. The check engine light was on for awhile but not now. The noise sound like its skipping.
Try this solution first, it may take care of all three codes for you and is a common issue on the G6 : http://www.g6ownersclub.com/forum/showthread.php?t=12532 The skipping might be the misfire caused by the faulty solenoids. Otherwise, the cat. converter may be fouling and throwing all the codes.