The throttle is designed not to work while the hand brake is engaged. If the hand brake is broken or the brake line is rusted (causing a loss of tension in the hand brake) the e-brake may stay engaged even when not being used. A sign to look out for is the rear tale light (brake light) flashing even while the hand brake is not being used. If the brake light is flashing then the e-brake is likely engaged.
Replacing Hand Brake is the best remedy to this issue. Sometimes, this issue may instead require a new a simple adjustment to restore tension in the brake line or possibly an entire new brake line if the current one is too rusted.