Help with LM35 fan I2C LCD project

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Yes, if I run a code where it detects the temperature only it works fine, if I power on the circuit (with the fan and everything) with only a USB it also works fine- issue being that since its only 5V its not powering on fully. The main issue starts after i plug in the DC power adapter to power on the fan fully.

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Also I added in a 1k Ohm resistor to the output of the LM35 in case it might work and added some more stuff into the code :

#include <LiquidCrystal_I2C.h>

//  LCD Setup 
LiquidCrystal_I2C lcd(0x27, 16, 2);  //address is 0x27

// Pin Definitions 
const byte sampleBin = 8;
const int tempPin = A0;     // LM35 out
const int fanPin = 9;       //  PWM control
const int ledPin = 6;       // LED

// Calibration Constants 
const int8_t fudge = 90;      // Adjust this for calibration (±5~10 usually fine)
const int kAref = 1090;       // Analog reference voltage in mV (1.1V = 1100mV)
const int kSampleBin = sampleBin * 1000; 

//  Temperature&Controlvars 
int tempC, tempF;
int pwm;
bool fanOn = false;
uint32_t temp = 0, start = 0;
const int interval = 500;  // Refresh rate 

void setup() {
  analogReference(INTERNAL);
  analogRead(tempPin);  // Dummy read

  // Pre-fill temp with average of 8 samples
  for (int i = 0; i < sampleBin; i++)
    temp += analogRead(tempPin);

  lcd.init();
  lcd.backlight();

  pinMode(fanPin, OUTPUT);
  pinMode(ledPin, OUTPUT);
  Serial.begin(9600);
}

void loop() {
  if (millis() - start > interval) {
    start = millis();

    //  average of samples
    temp -= (temp / sampleBin);
    temp += analogRead(tempPin);

    // Convert to °C 
    tempC = temp * kAref / (kSampleBin + fudge);
    tempF = (tempC * 18 + 3200) / 10;

    // LCD Display 
    lcd.setCursor(0, 0);
    lcd.print("Temp: ");
    lcd.print(tempC / 10);
    lcd.print(".");
    lcd.print(tempC % 10);
    lcd.print((char)223);
    lcd.print("C    ");

    // Fan Control with Hysteresis 
    if (!fanOn && tempC >= 160) {       // 16.0°C
      fanOn = true;
    } else if (fanOn && tempC <= 140) { // 14.0°C
      fanOn = false;
    }

    pwm = fanOn ? map(tempC, 150, 450, 100, 255) : 0;
    pwm = constrain(pwm, 0, 255);
    analogWrite(fanPin, pwm);

    //  Overheat LED 
    digitalWrite(ledPin, tempC > 400 ? HIGH : LOW); // 40.0°C threshold

    // Serial Debug 
    Serial.print("ADC: ");
    Serial.print(analogRead(tempPin));
    Serial.print(" | Temp: ");
    Serial.print(tempC / 10);
    Serial.print(".");
    Serial.print(tempC % 10);
    Serial.print(" C | Fan PWM: ");
    Serial.println(pwm);
  }
}