Hi,
I just tried to play this game in LAN with my bro, but I didn't find a button for that, and the other buttons didn't let us play either. Is there a way to do that? An unofficial patch, maybe?

The game should have lan, are you saying you can't find a lan option from any of the menu screens?

Exactly. The TCP/IP option takes me to a non-functional server browser (after asking for a TCP address) and the Modem option let's me choose a port (com1 - 4) and a speed and has "host" and "join" buttons. I couldn't get this to work either. The other two buttons do nothing, and in addition to them there's also a boatload of online multiplayer services listed (such as TEN). But no LAN option.

Back in the day when I played it with friends, we took the "Serial connection for direct play" option. Although that would imply that you don't need any router/switch/hub to play just between two computers, that was not the case. We had to put a hub in-between and then the games detected eachother.
Don't ask me the mechanics of that, because I don't know, just telling you what worked for me.

It should work if you go through the TCP/IP option. Just put in your friend's ip or no ip to let it search.
If that fails then I suggest you google GameRanger. It's helped me before to LAN old games.

It works fine for me. You need to select TCP/IP. It will ask you to insert the IP address or to leave blank to search. Just hit enter and then host a game. The game should appear for your brother to join. Make sure you don't have a firewall blocking you or anything like that.
I have played over LAN. Also played using Hamachi. I use Vista and have had no problems, just follow the instructions I posted above - it should be fairly simple.

To be clear, are you saying that you have successfully played via LAN with this version of TA? What version of Windows are you using?

Actually, I was using the original CD copies, which I still own. However, I'd imagine that this version would work just as well or better than the original copies, considering the work they put in on compatibility here at Gog. I installed the version I bought on Gog.com yesterday and was going to play it last night, but the friend I was going to do it with had something come up.
I'll tell you what, I will test the Gog version right now between my laptop and desktop and report the results. Both computers use Windows Vista service pack 2 - laptop is 64 bit and desktop is 32.
Tested and works fine. Choose TCP\IP, leave blank and press enter to search, select new game. The person joining will need to wait until they see the game and then join it.
Did you figure this out yet? Were you typing anything in when it asked for a TCP address or just leaving it blank? Mine doesn't take me to any sort of browser, but I just leave it blank to let it "search". It should be taking you to a lobby to host or join a game.

I've tried to get this bugger working with my friend vanilla, over Hamachi and with Game Ranger, none of them worked. With vanilla and Hamachi it just didn't find anything and with the Game Ranger my friend and I both got lobby connecting timeouts when trying to join each other's games. We even tried using the port-forwarding (2300-2400 and 16000 (for game ranger)) without much success. Running out of ideas here.. (yes, hamachi is located as the primary connection)

What multi-player option did you select? Do you have problems using LAN's for any other games?

The only feasible option for me was the TCP/IP as there was no LAN option. Usually LAN works just fine for me and I've played other games a number of times with it.

TCP/IP allows you to use it on a LAN.
Edit: I was unable to get this working across two computers here, with the GoG version, but I don't know if it was because one of them was running the game via Wine, where the DirectPlay is wonky, or if DirectPlay is broken on newer Windows systems as well.

I played the original TA and the gog version over LAN and internet just fine. All you need to do is:
0. make absolutely sure that your firewall and antivirus allows connecting to the host machine and the router doesn't filter out the game packets
1. choose multiplayer
2. tcp/ip
3. host the game on 1 machine, note it's ip address (lan, public or hamachi ip)
4. when asked for the ip in the game put there the hosts ip
5. start the game and play ;-)
points 0, 3 and 4 are essential to your success.

You can also leave the IP address blank to let it search for the host machine. Otherwise, I would follow cyberkiller's advice exactly.