In the magenta mode, you can easily check that the motors work: the robot should drive straight forward if you press forward, straight backwards if you press backwards. If you suspect a hardware issue, please refer to this procedure.
If in the red, yellow or green pre-programmed behaviours, the robot seems to detect your hand (indicated by light and sound) but does not move, it can probably not detect the ground. In those modes, Thymio is programmed to stop at the edge of the table. If you place it on a surface that does not reflect IR light (such as a black or dark surface, a transparent surface, some carpets) the surface is not detected and the robot stops. Try it on a white surface; If it still does not move then, there is probably a problem with the ground sensors. If you suspect a hardware issue, please refer to this procedure.