Your arduino code does not check if there is a character on the serial port, check - Serial.available() - Arduino Reference
#DEFINE LEDPIN 13
char val;
void setup()
{
Serial.begin(9600);
pinMode(LEDPIN , OUTPUT);
}
void loop ()
{
if (Serial.available() > 0)
{
val = Serial.read();
if (val == '0')
{
digitalWrite(LEDPIN ,LOW);
}
if (val == '1')
{
digitalWrite(LEDPIN ,HIGH);
}
}
}