Since the user:pass variable was disabled in IE, does anyone have a new code to make a webmail login page for cPanel webmail (ie. neomail, horde, or squirrelmail) WITHOUT a dialog box popping up to ask for username and password?

Something like this?

<form action="http://host.sld.tld:2095/login/" method="POST">
Username <input type="text" name="user" />
Password <input type="password" name="pass" />
<input type="submit" name="login" value="Login" />
</form>

It's really a tradeoff between IE's new 'security' method and 'how it used to work'.

If you mean if there is another method to do this:
http://user:pass@site.com/

to log into pass protected sites, no - not that I know of...

However, you can change the Windows registry so that this 'new method' is disabled:

http://support.microsoft.com/default.aspx?scid=kb;%5Bln%5D;834489

I kind of like how Firefox does it, it asks you if you want to log into the site using the login information.