I have the following problem

I have a laptop with windows which I use at work and at home. At work, my network admin has port 25 blocked.
Back home my ISP does not have port 25 blocked and I have a Linux server through which I connect to the internet. I have a public IP.

How can I set up some rules in my linux router, such that I can send from my laptop emails through port 25 from work ?

Network managers ususally block port 24 because it allows outgoing mail with no authentication and Spammers love to put a zombie on the hard drive to send out spam through port 25.
Usually there is a requirement to change the outgoing mail port (SMTP) to port 587 because it will allow authenticated smtp traffic.

So if you are able to send mail at work then you are probably configured for 587 or maybe 465 so you need to know what port you are configured for and set up you home system to open up that port.

What mail client are you using? and do you know how to go into the mail client configuration to discover which smtp port it is configured for?

It seems like you could set up an alternative mail client for use at home that would have port 25 in its configuration

My email client in microsoft outlook.
The mail server which I want to use is mymail.brinkster.com . The thing is that when I configure port 587 for mymail.brinkster.com it can't connect to it.

are they blocking 587 at work as well?
Are you blocking 587 on your Linux Box?

Your network guy at work is probably blocking ALL ports that are not required, inbound and outbound.. port 25 is probably only allowed to the corporate mail server, but not from clients to mail servers on the Internet. then only allowing a few other ports that are necessary for business purposes. at least that is the correct way to secure a network.

Open ports are going to be things like 80, 443, and probably not much more than that.. possibly ftp, and ssh.. I think you will find most other ports are blocked, if your network guy is doing his job properly.

so what's wrong with using the webmail interface on that zimbra server (mymail.brinkster.com) ? Zimbras webmail interface is well done and full featured.