Here is the solution I went with. Thanks to everyone for their assistance. It is very appreciated!

In my HTML::Template, I have a login section. If you are not logged in (ie, we can't find a session_id cookie in your browser), we send the following to your browser:

[HTML building some tables and the top-of-page navigation]

<SCRIPT TYPE="text/javascript" LANGUAGE="JavaScript">
function fill_in_screensize() {
     document.forms['login_form'].screen_width.value=screen.width;
     document.forms['login_form'].screen_height.value=screen.height;
     return true;
}
</SCRIPT>

<FORM name=login_form ACTION=[ACTION] METHOD=[METHOD]
<input type=hidden name=screen_width>
<input type=hidden name=screen_height>
[input fields for username and password]
<input type=submit value="submit" onClick='fill_in_screensize();'>
</FORM>
[download]

Then, in my perl code, I grab the values with $query->param('screen_width'), dbh->quote it and then stuff it into the user's account record along with the other data I track (ip_address, user-agent string, etc).

I don't believe WebTV supports Javascript but since WebTV displays at less than 544 pixels wide, I can just parse for WebTV user-agent strings to get an idea of how many usrs have a resolution under 640x480.

Wow! The first time Javascript has served a useful purpose in all my years!