Pin mode is always LOW when it should be HIGH - arduino

Question

I'm working with simple Arduino where I'm trying to turn on a LED light by using serial print and turning off the LED Light when I click the button or use the switch on the board, when the pin is in the ground.
At the moment, I can turn on the led light by serial, however when I click the button the LED light will switch off but then never switch on, and that's happening because the state is being stuck at low all the time and never switching back to high.
Here's the code:
// constants won't change. They're used here to
// set pin numbers:
const int buttonPin = 2; // the number of the pushbutton pin
const int ledPin = 3; // the number of the LED pin
int state = 0;
// variables will change:
int buttonState = 0; // variable for reading the pushbutton status
void setup() {
// initialize the LED pin as an output:
pinMode(ledPin, OUTPUT);
// initialize the pushbutton pin as an input:
pinMode(buttonPin, INPUT);
Serial.begin(9600);
}
void loop() {
// read the state of the pushbutton value:
buttonState = digitalRead(buttonPin);
if (Serial.available())
{
state = Serial.parseInt();
if (state == 1)
{
digitalWrite(ledPin, HIGH);
Serial.println("ON");
}
}
// check if the pushbutton is pressed.
// if it is, the buttonState is HIGH:
if (buttonState == LOW) {
state = 0;
// turn LED OFF:
Serial.println("off");
digitalWrite(ledPin, LOW);
}
// IMP : This Never runs. the state is always off therefore when i send to serial " 1" the led just blinks
else {
Serial.println("off");
}
}
The state is always off therefore when I send to serial " 1" the LED just blinks

Answer 1

I think you are reading state from PIN using wrong function.
if (Serial.available())
{
state = Serial.parseInt();
Why not use https://www.arduino.cc/reference/en/language/functions/digital-io/digitalread/ ?
Are you sure this condition is evaluated to true? if (Serial.available()) ?

Answer 2

You are making the logic too much complicate. Just check the serial if it is available and have the desire value turn led on else check the button and if it pressed turn the led off. On other conditions DO NOTHING. That is all you need.
// set pin numbers:
const int buttonPin = 2; // the number of the pushbutton pin
const int ledPin = 3; // the number of the LED pin
int state = 0;
// variables will change:
int buttonState = 0; // variable for reading the pushbutton status
void setup()
{
// initialize the LED pin as an output:
pinMode(ledPin, OUTPUT);
// initialize the pushbutton pin as an input:
pinMode(buttonPin, INPUT);
Serial.begin(9600);
}
void loop()
{
if (Serial.available())
{
state = Serial.parseInt();
if (state == 1)
{
digitalWrite(ledPin, HIGH);
Serial.println("ON");
}
}
// check if the pushbutton is pressed.
// if it is, the buttonState is HIGH:
else if (digitalRead(buttonPin) == HIGH)
{
// turn LED OFF:
Serial.println("off");
digitalWrite(ledPin, LOW);
}
}