RequiredFieldvalidator

I would suggest you to write javascript code to achieve this:
Its pretty simple. Do something like this

function validateTextboxes()
        {
            if((document.getElementById('txtbox1').value == "") && (document.getElementById('txtbox2').value == "") && (document.getElementById('txtbox3').value == "") && (document.getElementById('txtbox4').value == ""))
            {
                alert('alert msg');
                return false;
            }
            
            else
            {
                return true;
            }
        }

Call the function onClientclick of button.. something like this:

OnClientClick="return validateData();"

On server side do the same checking before doing operations so that if javascript is diabled, validation is still performed.

Hope this helps!!!