My car will idle but nothing more when you push accelerator

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.