First of all, have you powered your arduino board properly.?
If yes,
You need to check pwm signal output (orange wire) from arduino board using oscilloscope, is it present pulsed signal on it (pwm signal), or not?
Then,
If the signal not presents, the problem is on your arduino board.
1. measure analog in (yellow wire), the voltage must change simultaneously when you turns left or right the potentiometer.
2. verify the code was downloaded properly into your arduino board.
3. except 2 points above, you have damaged chip.
If the signal presents,
1. check pwm frequency, L293D can support up to 5kHz switching frequency.
2. check pwm duty cycle, pwm duty cycle must change when you turns left or right the potentiometer. if it's not, verify the code.
larger duty cycle = run faster.
You can using regular DC motor <1A for that application.