Eh, well you should not edit that file...
DotNetNuke has parts that are customizable and parts you should not customize.
The part you should not customize we refer to as the "Core".
Your change is a Core change which is a problem because the file gets overwritten if you upgrade DNN.
(And you would have to go back in and change the file again)
The design of your website including what icon to use for the search dropdown is called a skin in DNN.
In the skin there's a reference to the file you changed, with some attributes to set how it should be rendered.
As an example:
Open this folder
\Portals\_default\Skins\
You will see one or more folder there, these are skin folders.
(you can have several skin packages installed)
Now open the "DarkKnight" folder (I'm guessing your using DNN 6)
All the files in this folder are called a Skin package, which makes the visual appearance of your website.
This we call a skin folder.
The .ascx files you see are the actual skin version.
One of these ascx files is the file that get loaded as the skin, for every skin you can choose in DNN, there's an ascx file (with configurations HTML elements etc.)
Example:
If you open the file:
Home-Mega-Menu.ascx
It contains HTML and some special elements called skin objects.
In that file you will find this line:
<dnn:SEARCH ID="dnnSearch" runat="server" UseDropDownList="true" EnableTheming="true" Submit="Search" />
This is a reference to the file you edited.
Here you can set it's properties, to determine how search box should be rendered.
The advantage of this is that a skin designer can determine if he wants to use the site icon or a custom icon. So if you would want the behaviour you want, you would change the line to:
<dnn:SEARCH ID="dnnSearch" runat="server" UseDropDownList="true" EnableTheming="true" Submit="Search" SiteIconURL="~/Portals/0/favicon.ico" />
The advantage of that is that a skin / site designer can choose what icon to use...
And you can have different skins with different behaviour, your change (apart from the upgrade issues) will set the same behaviour for all skins / site in a DNN installation, which is less flexible.
I hope it's clear.
Timo