IE Not Sending Cookie Info To Server

I am developing an asp.net 2.0 application using visual studio 2005 on my
computer and I am getting very inconsistent results when I test on my
computer versus from other computers.

The symptom of the problem is that the web server does not receive cookie
information from the browser after I have properly logged in to the web
server. Without this information, my session state keeps on getting lost and
the authentication logic sends me back out to the login page.

Using Fiddler, I have narrowed down the problem to what I think is the
browser not always sending cookie information (containing the session and
authentication ticket) to the web server.

This is what I have tried:

1. If I run the browser on the same computer as the webserver, I see that
the cookies are sporadically not being sent from the browser for the .aspx
pages.

2. If I run the browser from a 2nd and 3rd computer and hit the web server
on the first computer, I see that the cookies are always being sent for the
..aspx pages.

3. If on the webserver I force asp.net to assume cookieless clients, my
browser on the same computer works fine since the "cookie" information is
part of the URL.

I haven't tried installing my dev environment on the 2nd or 3rd computers
and try to see how the browser behaves when hitting the new webserver. I am
trying to avoid that for now. But from my 1st computer, if I run the browser
against a totally different web application I have seen the same behavior in
my Fiddler logs. The browser sporadically does not send cookie information
to the server.

I suspect that it may be something specific to the IE browser on my
computer. Maybe there is some security program or setting that is causing
this issue on this computer and not others. Does anyone have any thoughts or
ideas on what this problem could be? I want to find out the problem to make
sure that when I deploy my web application, this issue does not resurface on
my user's computers.