I had put a semi-colon at the end of the "protected void output(String value)" declaration. I removed it, but I also restarted Visual Studio and it worked fine, finally. It might have been that one "schtupid" semi-colon.

Thanks!

using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;
using System.Web.UI;
using System.Web.UI.WebControls;
using System.Text;

public partial class ProgrammingCSharp : System.Web.UI.Page
{
    protected void Page_Load(object sender, EventArgs e)
    {
    }

    protected void output(String value)
    {
        outputText.Text += value + Environment.NewLine;
    }

    protected void clearButton_Click(object sender, EventArgs e)
    {
        outputText.Text = "";
    }
    protected void runButton_Click(object sender, EventArgs e)
    {
        outputText.Text = "Hello World!";
    }
    protected void outputText_TextChanged(object sender, EventArgs e)
    {

    }
}