How can I make this C# code less processor-intensive?

Since you'll have "hundreds, maybe thousands of commands" then I'd suggest using a Dictionary<string, string>. Something like:

private static Dictionary<string, string> CommandMap = new Dictionary<string, string>(StringComparer.OrdinalIgnoreCase) {
    { "Help", "Type a command!" },
    { "Quit", "Goodbye!" },
    { "MyCommand", "My Command response" },
    // etc... { commandstring, responsestring }
  };
public static string ParseCmd(string rawCmd)
{
  string response;
  if (!CommandMap.TryGetValue(rawCmd, out response)
  {
    // here's where you could respond to an unrecognized command
    // or you could just let ParseCmd return null and handle it somewhere else.
  }
  return response;
}

But you implied that you had subcommands so you might need to have a different structure, where each top-level command returns the information necessary to parse the specific subcommand. What that information is depends on what you're doing.
I suspect some sort of tree structure.

If you start to check for cases, you need to check all combinations.
help, helP, heLp, heLP, hElp, hElP, hELp, hELP, Help, HelP, HeLp, HeLP, HElp, HElP, HELp and HELP.
The best solution is to force to lower case or upper case, your choice.

public static String ParseCmd(String rawCmd)
        {
        string TmpCmd= rawCmd.ToUpper();
        if (TmpCmd.Equals("HELP")
        {
            return "help!";
        }
        else if (TmpCmd.Equals("QUIT")
        {
            return "Quit!";
        }
        else if (TmpCmd.Equals("MYCOMMAND")
        {
            return "My Command!";
        }
        else
        {
            return "Unknown Command!";
        }
        return null;
    }

[Update]
if and switch perform the same. The difference is that if allow more sophisticated conditions.
For hundred or thousands of commands, other techniques are to be used to prevent having to check every possibilities.
More details would be needed to determinate which technique is best.

You can do like below...

if(rawCmd.ToLower().Equals("help")){
    // Codes here
}