Before making any attempts to change something, contact your network administrator and ask him the same question.
The most likely reason you cannot update your Windows machine, is because your user account there does not have the required privileges to do so. In order to perform updates on Windows, you must be logged in with the Administrator account -or an account that is part of the Administrators group.
If the access to Windows Update services is actually blocked on network level by the network administration personnel, I'm sure there might be a good reasons for that. You see, the maintenance of systems is their job -I am sure you wouldn't like if someone interfered with your job and made a mess out of it. Neither would they.
On the other hand, there is a good chance that something like this can be caused by malware infection. Try scanning your systems with antivirus software. Also, you could take a look at your hosts file, and check if Windows Update hostnames are mapped for example to localhost, or some other IP addresses other than the actual Windows Update servers.