I had a similar problem from work, and it turned out that they have some sort of firewall or other security in place which does not allow ssh traffic out. I was able to do it from reflectionx, which is an xterm emulator for winblows, but had to do a runsocks command preceding the ssh command in order to get out. Putty simply will not work, and IT guys told me there's nothing I can do about it.
Point is, it could just be the LAN at your work blocking you. I too run httpd and can, of course, always get to the website from anywhere. It not only uses a different port ( which is allowed out of the network) but obviously different protocols and security measures.
Good luck anyways...