How do I run a Python script from C#?

The reason it isn't working is because you have UseShellExecute = false.

If you don't use the shell, you will have to supply the complete path to the python executable as FileName, and build the Arguments string to supply both your script and the file you want to read.

Also note, that you can't RedirectStandardOutput unless UseShellExecute = false.

I'm not quite sure how the argument string should be formatted for python, but you will need something like this:

private void run_cmd(string cmd, string args)
{
     ProcessStartInfo start = new ProcessStartInfo();
     start.FileName = "my/full/path/to/python.exe";
     start.Arguments = string.Format("{0} {1}", cmd, args);
     start.UseShellExecute = false;
     start.RedirectStandardOutput = true;
     using(Process process = Process.Start(start))
     {
         using(StreamReader reader = process.StandardOutput)
         {
             string result = reader.ReadToEnd();
             Console.Write(result);
         }
     }
}

If you're willing to use IronPython, you can execute scripts directly in C#:

using IronPython.Hosting;
using Microsoft.Scripting.Hosting;

private static void doPython()
{
    ScriptEngine engine = Python.CreateEngine();
    engine.ExecuteFile(@"test.py");
}

Get IronPython here.