2007 Toyota Corolla I have problem with my Corolla

Heyy I have a toyota corolla 2007. And I have problem with this car. The problem is when we start the car and we put the gear to reverce or drive the car shaking reallt well. And also when we drive on the drive gear and when they change the each gear, its feels like something is pushing me from the back and its be like a quick shake when they change the gear. Their engine check light is on too.I don't know what is the problem iss. Can u pleasee find out for me what is the problem is. And that will be great helpful and I will rellay apreciate that.

updated 3/1/10

haai the code number is 2716