Do you have the grounds connected? It's not drawn in that Fritzing. Without that, it won't work ever.
If so: measure the voltage on the output pins of the Arduino - is it what you expect? If not: software issue, or Arduino broken.
If OK: measure the voltage on the input pins of the L298N - again, is it what you expect? If not: faulty connection.
If OK: measure the voltage on the output pins of the L298N (without motors). Is it what you expect? If not: chip broken.
If OK: measure the voltage at the motor pins. Is it what you expect? If not: faulty connection.