DVD Stepper nor working

Hello everyone!

I recently scavenged some DVD readers for their steppers. It's somewhat ike this:

I soldered some wires directly to them and tested with a LiPo cell because I don't have a multimeter. The stepper moves forward with these sequence:

-1 to positive and 2 to negative.
-3 to positive and 4 to negative.
-1 to negative and 2 to positive.
-3 to negative and 4 to positive.
-REPEAT


Next I made this circuit (yes, with actual LEDs) using a TD62783AP as driver.

void setup() {
    
    // put your setup code here, to run once:
    pinMode(10, OUTPUT);
    pinMode(11, OUTPUT);
    pinMode(12, OUTPUT);
    pinMode(13, OUTPUT);
    //
    digitalWrite(10,LOW);
    digitalWrite(11,LOW);
    digitalWrite(12,LOW);
    digitalWrite(13,LOW);

}

void loop() {
    
    //1000
    digitalWrite(10, HIGH);
    digitalWrite(11, LOW);
    digitalWrite(12, LOW);
    digitalWrite(13, LOW);
    //
    delay(500);
    //0010
    digitalWrite(10, LOW);
    digitalWrite(11, LOW);
    digitalWrite(12, HIGH);
    digitalWrite(13, LOW);
    //
    delay(500);
    //0100
    digitalWrite(10, LOW);
    digitalWrite(11, HIGH);
    digitalWrite(12, LOW);
    digitalWrite(13, LOW);
    //
    delay(500);
    //0001
    digitalWrite(10, LOW);
    digitalWrite(11, LOW);
    digitalWrite(12, LOW);
    digitalWrite(13, HIGH);   
    delay(500);

}

With this code the LEDs light in the correct order: LED1, LED3, LED3, LED4. Now if I replace the LEDs with the stepper windings, it doesn't work (or if I connect the LEDs to the IC outputs as if they were windings) so I know I'm doing something wrong, most likely because I don't understand how the IC works. Any help?

You need a bidirectional current driver to drive a four wire stepper.

The TD62783 can only source current, so it won't work.

Understood. Could you explain (I don't know electronics) in a simple way why it dosn't work as I expected?
For me it was like "this output is low, that one is high, current should flow".

Low output is not a GND. Have a search on H bridge. Compare it with your circuit.

Just use a stepper driver chip. For low power steppers, such as that one is very likely to be, even the ancient L298 or L293D will work.

Understood. Could you explain (I don't know electronics) in a simple way why it dosn't work as I expected?

Because the motor has two coils in it, and not only do you have to control if the current is flowing or not but you have to control in which direction it is flowing. You can not do that with your circuit you can only do the flowing or not bit.
The direction of current flow determines the polarity of the magnetic field the coil generates.

Made this H-bridge:

With IRF1404 and IRF9540. MOSFETs powered by a 3.7V LiPo cell. I can hear a low "click" sound in the motor, but it doesn't step.

With IRF1404 and IRF9540.

Wrong MOSFETs. You need logic level MOSFETs.

This will be a long learning journey.

Keep in mind that most “Instructables” are pure crap, written by people who have no clue what they are doing, but are happy to deceive others with their ignorance.

Made this H-bridge:
http://www.instructables.com/id/Bipolar-Stepper-Motor-Driver/

Very very bad design.
This joker can't even draw a schematic so that tells you he is an idiot. Even with a barge pole don't go their.

The main problem is their is no protection for shoot through, that is both FETs can be on at the same time resulting in a very large current. Also you can not use driving voltages higher than the signal voltage, and their is no protection for the large charging currents on switching and nothing to stop chaos on switch on when all the pins are in effect floating until the boot loader is finished.

Designing a decent H-bridge circuit is difficult, all those with just FETs or transistors are rubbish.

A4988 or DRV8825 drivers with 12V supply will probably do the job far better than other simple approach,
so long as you can estimate the motor's current rating. What is the winding resistance of the motors?