Change value of input and submit form in JavaScript

You could do something like this instead:

<form name="myform" action="action.php" onsubmit="DoSubmit();">
    <input type="hidden" name="myinput" value="0" />
    <input type="text" name="message" value="" />
    <input type="submit" name="submit" />
</form>

And then modify your DoSubmit function to just return true, indicating that "it's OK, now you can submit the form" to the browser:

function DoSubmit(){
  document.myform.myinput.value = '1';
  return true;
}

I'd also be wary of using onclick events on a submit button; the order of events isn't immediately obvious, and your callback won't get called if the user submits by, for example, hitting return in a textbox.

document.getElementById("myform").submit();

This won't work as your form tag doesn't have an id.

Change it like this and it should work:

<form name="myform" id="myform" action="action.php">