I am just coming into this, however with your GoDaddy account, is it a straight Windows Shared Hosting plan? Or is it a Virtual Host?
If it is a shared hosting plan, you won't be able to install Apache, or WAMP, if I am not mistaken.
If you have administrative privileges and/or its dedicated / virtual dedicated, you can install it.
If this is the case, the easiest method would be to disable the IIS Web Service, this can usually be done by the IIS Snap-In from the administrative Tools.
You would have to disable the default website, you can at that point, install Apache, MySQL, and I would also recommend an FTP server as well
Under your control panel you will see Administrative Tools,
You should see Internet Information Services (IIS) Manager, or something similar (I only have a Win2k3 server here to compare)
Once you are in there, you can expand the tree, you should see ???? (local computer), expand, and at least in W2k3, it has "Web Sites" as a folder, expand that.
From there you can right-click any site and click "Stop". This will allow you to build & test your apache configuration before permanently disabling IIS.
If you are satisfied with your apache setup, but still don't want to completely uninstall IIS, you can go into your services (Start, Run, then type: 'services.msc') Or Via your Control Panel.
Look for "World Wide Web Publishing Service", right click -> properties (or double click that service).
Set Startup Type to Manual or Disabled, then ensure you have Service Status as Stopped.
As goes for the installation of Apache, PHP, MySQL, phpMyAdmin, etc google can point you to TONS of tutorials to help you along.
Also noteworthy:
If you have a control pane with this (virtual) dedicated hosting, it may no longer work for many services or break all together if you change the configuration that it knows, in fact if its running off of IIS (as it most likely is) it won't work at all.
The best solution: Disable Directory Browsing (should be by default) and put a blank/empty index.asp / index.php / index.htm / index.html in that folder.
And for Login & Password type security, look at PHP MySQL Login System in google.
If you are on shared hosting, the above just won't work, and you will have to look through your control panel to see if they offer directory security, or do a script based login system (doesnt protect directories, however).