Visual Studio C#/.NET Interfacing with Arduino

Hi everyone, this is my first post (I hope I have the right sub-forum) and I am having some trouble programming in Visual Studio 2012 with C# Interfacing with an Arduino UNO (SMD edition). Apologies if this is an extremely "nooby" question, I am still new to this.

The issue I'm having is that I can't seem to get LED Pin 13 to blink or adjust turning it off and on manually using my C# code (buttons on the form), but I know Pin 13 LED works because It runs normally using Arduino IDE's Blink example sketch, and it's solid and on when the Arduino is plugged into my laptop.

However, what does happen when I run my C# and click the button I made is that the "RX" light blinks once very quickly, then nothing. I have googled around for hours but none of the examples I find seem to work for me. And all the examples I find don't seem to have any mention towards pin 13, but still work for some reason (for them). By now it might be obvious that I am new to Arduino, but the help would be most appreciated :)!

Here's my C# program (sorry if it's a bit of a mess):

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Text;
using System.Windows.Forms;
using System.IO.Ports;


namespace ArduinoBlink
{
    public partial class Form1 : Form
    {
        SerialPort serialPort = new SerialPort();
        
         public Form1()
         {
             InitializeComponent();

             serialPort.PortName = "COM4";
             serialPort.BaudRate = 9600;
             serialPort.DtrEnable = true;
             serialPort.Open();
             

         }

//Will close the port when the program is closed and no longer being used
        private void Form1_FormClosed(object sender, FormClosedEventArgs e)
        {

            if (serialPort.IsOpen)
            {
                serialPort.Close();
            }
            
        }

//Want LED pin 13 to turn on (or blink, whatever)
        private void ButtonOn_Click(object sender, EventArgs e)
        {
            serialPort.Write("1"); // Send byte '1' to the Arduino
            textBox1.Text = "THE LED IS ON";//tells the user that the led is ON     
        }
    }
}

Edit: I should also add that when I start my program (before I click any buttons), pin 13 DOES blink 3 times quickly. After that, the LED 13 pin light L lights up and stays solid. When I click the button I have on my program, it only lights up the RX LED.

What is the code running on the arduino

I assume that "serialPort.Write("1")" sends the character for "1" to the Arduino rather than a byte with thee value B00000001

Is that what the Arduino is expecting?

Your comment in the C# code is ambiguous.

...R