How to allow user to search without refreshing the page

Question

I think what do you want is this.

You need set how updatePanel´s trigger the button.

The part of page what do you want update need to be inside the updatepanel.

The javascript will catch DropDownList changes, and after all three DropDownList were changed the postback will be raised like if you was clicked in button

aspx

<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="//ajax.googleapis.com/ajax/libs/jqueryui/1.10.4/jquery-ui.min.js"></script>
<script>
    var slcLocationSelect = false;
    var slcSpecialtySelect = false;
    var slcGenderSelect = false;
    $(document).ready(function () {
        $("#<%=slcLocation.ClientID %>").change(function () { changeDropDown(this) });
        $("#<%=slcSpecialty.ClientID %>").change(function () { changeDropDown(this) });
        $("#<%=slcGender.ClientID %>").change(function () { changeDropDown(this) });
    });
    function changeDropDown(sender) {
        if ($(event.target).attr('id') == $("#<%=slcLocation.ClientID %>").attr('id')) {
            slcLocationSelect = true;
        }
        if ($(event.target).attr('id') == $("#<%=slcSpecialty.ClientID %>").attr('id')) {
            slcSpecialtySelect = true;
        }
        if ($(event.target).attr('id') == $("#<%=slcGender.ClientID %>").attr('id')) {
            slcGenderSelect = true;
        }
        if (slcLocationSelect && slcSpecialtySelect && slcGenderSelect) {
            slcLocationSelect = false;
            slcSpecialtySelect = false;
            slcGenderSelect = false;
            __doPostBack("<%=LinkButton1.ClientID %>", "");
        }
    }
</script>
<div style="width: 390px; margin: 0 auto;">
    <asp:DropDownList ID="slcLocation" runat="server" ClientIDMode="Static" Style="width: 365px;"
        class="default" AppendDataBoundItems="true">
    </asp:DropDownList>
    <br />
    <br />
    <asp:DropDownList ID="slcSpecialty" runat="server" ClientIDMode="Static" Style="width: 365px;"
        class="default" AppendDataBoundItems="true">
    </asp:DropDownList>
    <br />
    <br />
    <asp:DropDownList ID="slcGender" runat="server" ClientIDMode="Static" Style="width: 365px;"
        class="default" AppendDataBoundItems="true">
        <asp:ListItem Text="Any Gender" Value="" Selected="True" />
        <asp:ListItem Text="Male" Value="1" />
        <asp:ListItem Text="Female" Value="2" />
    </asp:DropDownList>
    <br />
    <br />
    <div style="width: 390px; margin: 0 auto;">
        <asp:LinkButton ID="LinkButton1" runat="server" OnClick="LinkButton1_Click">Find</asp:LinkButton>
    </div>
    <asp:UpdatePanel ID="UpdatePanel2" UpdateMode="Conditional" runat="server">
        <ContentTemplate>
            <asp:Label ID="Label1" runat="server" Text="Label"></asp:Label>
            <div style="width: 100%;">
                <asp:Repeater runat="server" ID="rptContent">
                    <HeaderTemplate>
                        <table border="0" id="tblInfo" style="background: #43A79A; width: 100%;" clientidmode="Static">
                            <tr>
                                <td>
                                    Physician Name
                                </td>
                                <td>
                                    Image
                                </td>
                                <td>
                                    Gender
                                </td>
                                <td>
                                    Office1
                                </td>
                                <td>
                                    Office2
                                </td>
                                <td>
                                    Office3
                                </td>
                                <td>
                                    Office4
                                </td>
                            </tr>
                    </HeaderTemplate>
                    <ItemTemplate>
                        <tr>
                            <td>
                                <%# Eval("Physician Name").ToString() %>
                            </td>
                            <td>
                                <img src="www.site.com/<%# Eval("Image").ToString() %>" />
                            </td>
                            <td>
                                <%# Eval("Gender").ToString() %>
                            </td>
                            <td>
                                <%# Eval("Office1").ToString() %>
                            </td>
                            <td>
                                <%# Eval("Office2").ToString() %>
                            </td>
                            <td>
                                <%# Eval("Office3").ToString() %>
                            </td>
                            <td>
                                <%# Eval("Office4").ToString() %>
                            </td>
                        </tr>
                    </ItemTemplate>
                    <FooterTemplate>
                        </table>
                    </FooterTemplate>
                </asp:Repeater>
            </div>
        </ContentTemplate>
        <Triggers>
            <asp:AsyncPostBackTrigger ControlID="LinkButton1" />
        </Triggers>
    </asp:UpdatePanel>
</div>

cs

protected void LinkButton1_Click(object sender, EventArgs e)
{
    Label1.Text = slcGender.SelectedItem.ToString();
}