I am sending my diagram for connection of the driver SN754410 to arduino for control of a DC motor. It is the same like yours. The pins 1, 2, 7 are connected to Arduino. The logic supply of 5V is taken from Arduino too. The motor supply is taken from an adapter (9V/0.66mA). The ground is taken from Arduino too. But when I connect 9V to the pin 9, the connection between arduino and my PC stops, the screen of the monitor starts blinking. Something is wrong.
Sorry a totally inadequate diagram, it shows nothing.
Post a proper schematic showing the power supplies the motors and the Arduino.
Yes you have wired something wrong so first we must see what you are trying to wire, then only when that is correct we can concentrate on seeing if you have wired it like that.