how to enable/disable a button depending on the textbox text property

Try following demo, it may be helpful.

<input type="text" id="uxSearchText" onkeyup="changeState();"><input type="button" id="uxSearchButton" value="Search" disabled=disabled />
<script type="text/javascript">
    function changeState() {
        var val = document.getElementById('uxSearchText').value;
        if(val.length>0) {
            document.getElementById('uxSearchButton').disabled='';
        }
        else {
            document.getElementById('uxSearchButton').disabled='disabled';
        }
    }
</script>

Let me know if its not working.

There is another way also. Suppose you have Master page as Master.master and child page as Default.aspx. Do following changes in these pages step by step.
In Design of Master page you may have a button as below.

<asp:Button ID="uxSearchButton" runat="server" Text="Search" />

Add new public property in code behind file of Master page as below.

public Button SearchButton
{
    get
    {
        return this.uxSearchButton;
    }
}

In Design part of Default.aspx add MasterType as below.

<%@ MasterType VirtualPath="~/Master.Master" %>

You may have TextBox and script in Design part of Default.aspx as below.

<asp:TextBox ID="uxSearchText" runat="server"></asp:TextBox>
    <script type="text/javascript">
        function changeState(uxSearchText, uxSearchButton) {
            var val = document.getElementById(uxSearchText).value;
            if (val.length > 0) {
                document.getElementById(uxSearchButton).disabled = '';
            }
            else {
                document.getElementById(uxSearchButton).disabled = 'disabled';
            }
        }
    </script>

Add following lines in Page_Load event of Default.aspx page

Master.SearchButton.Attributes.Add("disabled", "disabled");
uxSearchText.Attributes.Add("onkeyup", string.Format("changeState('{0}', '{1}');", uxSearchText.ClientID, Master.SearchButton.ClientID));

Now run the page you will get the result as expected.

I think you missed following tag in Deafault.aspx

<%@ MasterType VirtualPath="~/Master.Master" %>

Here is complete code of Default.aspx design page.

<%@ Page Title="" Language="C#" MasterPageFile="~/Master.Master" AutoEventWireup="true" CodeBehind="Default.aspx.cs" Inherits="HostDevServer.Default" %>

<%@ MasterType VirtualPath="~/Master.Master" %>
<asp:content id="Content1" contentplaceholderid="head" runat="server" xmlns:asp="#unknown">
</asp:content>
<asp:content id="Content2" contentplaceholderid="ContentPlaceHolder1" runat="server" xmlns:asp="#unknown">
    <asp:textbox id="uxSearchText" runat="server"></asp:textbox>
    <script type="text/javascript">
        function changeState(uxSearchText, uxSearchButton) {
            var val = document.getElementById(uxSearchText).value;
            if (val.length > 0) {
                document.getElementById(uxSearchButton).disabled = '';
            }
            else {
                document.getElementById(uxSearchButton).disabled = 'disabled';
            }
        }
    </script>
</asp:content>

Code behind will be.

protected void Page_Load(object sender, EventArgs e)
        {
            Master.SearchButton.Attributes.Add("disabled", "disabled");
            uxSearchText.Attributes.Add("onkeyup", string.Format("changeState('{0}', '{1}');", uxSearchText.ClientID, Master.SearchButton.ClientID));
        }

I, hope it will work.