The Check Engine Light on so the computer in your car is going to have relevant information stored in its memory which will help figure out what is going on. A scan tool is needed to retrieve this information. A professional grade scan tool allows key engine sensor data to be analyzed right off the scan tool without having to do intrusive testing at each sensor. You will probably find a bad throttle body or pedal control switch.
I was a toyota service manager for 14 years. You most definately have a computer problem. On both the Matrix and corolla toyota had problems with them and there is a TSB for the repair. I do believe that they may have actually made it a recall. I would call your local dealer and give them your VIN# and they can find out if you need the updated computer in your car.