Drupal not able to make any outgoing HTTP requests

Question

So, my drupal setup is on a NAS architecture. It's a portal for a college department and is hosted on the campus NAS. This basically means that my web server has to connect through an internal proxy within the campus to be able to connect to the internet outside.

I have Drupal 7.16 and I've still not performed a core update to the latest version of 7. Here are the issues I'm facing:

1. No update status or available updates for any of the modules and core - My drupal is simply not able to receive any update information what so ever. I keep getting "No available updates found" or "No available update data" whenever I try to check manually

2. Not able to install any modules directly from the URL - Whenever I try to paste a module's url, I keep getting the following error: "HTTP error 110 - Unable to fetch package". I'm still installing all modules manually by extracting and moving them to the modules folder.

3. I have the module mollom installed to moinotr spam comments, but I haven't been able to get this module working. This is the error that I get when I go into mollom's configuration page: "The Mollom servers could not be contacted. Please make sure that your web server can make outgoing HTTP requests."

So, keeping these three issues in mind, I think the main issue is the fact that either my Drupal or my web server aren't able to make any outgoing HTTP requests to any URL.

Here's what I think could be the causes for this issue:

1. Proxy settings? - Should I change the proxy settings for drupal somewhere? I have Drupal 7.16 which doesn't have proxy support unless you install this patch: http://drupal.org/node/7881#comment-4134240 But installing the patch didn't make any difference. I still get those errors. Should I also be asking my system admin to setup a dedicated user for the drupal's proxy settings? How would this work?

2. Folder/file permissions - I've checked the folder permissions and don't think it's the issue here, but maybe I'm wrong

3. Apache not able to make outgoing HTTP? - Could this be an issue with Apache? I've also tried using wget on the server and it works without any issues. I also tried running a php script like this(since cURL is not installed on my server and I would have to ask my system admin for it):

   $content = file_get_contents('http://www.example.com/test.html'); var_dump($http_response_header);

This script ran without any errors whatsoever.

I'm really not sure what the issue is here, and when I go ask my system admin to add/remove packages or change config files, I need to be making some sense. So can someone please tell me what the issue I'm facing here is?

Thanks,

Kaushik