List the part numbers of your equipment please....
Speed control
Receiver
Radio controller
Servo
First, set your radio epa's to 100%, some radios goto 150% for steering and 160% for throttle and this can sometimes cause problems for some equipment. Check your radio to make sure their is no servo mixing enabled. Turn you dual rate to 100% as well, Trims to 0. Reset you speed control setup calibration.
See if problem still exists.
You mentioned when you return the steering to center the car moves forward. Does the car still move forward if you unplug the servo? does the throttle still not respond when you turn the controller wheel with the servo unplugged?
put your car up on a block and test the problem while unplugging the servo and plugging it back in, If the problem only happens while the servo is plugged in, try the same procedure with another servo to confirm if its a servo compatability issue.
Same thing with the receiver, if their is still a problem, move onto the radio...