Using a popup to display messages to the user
A few ideas:


Your three javascript functions could easily be combined into one with some simple arguments, like headerText, statusMessage, statusType.
In your description you list some success text, but this isn't in the javascript, so I guess this is set in the code-behind. I consolidate how the text is set. If you choose to use javascript, you could simplify things by changing the asp:Label to a span.
It might be nicer to put the style information in the CSS file and then in the javascript just toggle which classes apply.


Here's an example of how it might look:

CSS

#NewCustomerSubmitStatusPopup.successPopup
{
  background-color: white;
  border-color: #9cc3f7; /* width, pattern added to main CSS block */
}

#NewCustomerSubmitStatusPopup.successPopup h1, #NewCustomerSubmitStatusPopup.successPopup span
{
  color: #9cc3f7;
}

#NewCustomerSubmitStatusPopup.errorPopup
{
  background-color: #F7DFDE;
  border-color: #BD494A;
}

#NewCustomerSubmitStatusPopup.errorPopup h1, #NewCustomerSubmitStatusPopup.errorPopup span
{
  color: #BD494A;
}


javascript

function ShowSubmitPopUp(headingText, statusMessage, statusType)
{
    $('#NewCustomerMask').show("slow");
    $('#NewCustomerSubmitStatusPopUp').show("slow");

    var popupClass = (statusType == 'error' ? 'errorPopup' : 'successPopup');
    $('#NewCustomerSubmitStatusPopUp').attr('class', popupClass);
    $('#NewCustomerSubmitStatusPopUp h1').html(headingText);
    $('#NewCustomerSubmitStatusPopUp span').html(statusMessage);
}