problem:when he ''shut down'' the laptop I can not connect remotelly to his laptop anymore,how to fix that?
Are you saying you want to connect to his system when its been shut down or after a shutdown and reboot it no longer works?
Port 3389 is the common RDP port so wondering why your using RDP between 2 computers in the same room?
Are you trying to connect with internet connection sharing where his laptop gets an internet connection and then you can then connect thru his laptop as the gateway shared internet connection or are you two using RDP ( Remote Desktop ) between both systems in which only 1 person can use each computer at a time because the one that is in use remotely by the other is unusable. *Last i knew RDP only allows 1 person at a time to use workstation based OS's. Its only on the server side of things that you can have terminal sessions with multiple people sharing a single system.
https://en.wikipedia.org/wiki/Remote_Desktop_ServicesLastly being in the same room you would connect over the LAN, you wouldnt go over the WAN out through router and back to your brothers computer. You would simply know that your brothers computer is at a specific IP or Name and connect to it that way. Setting up the laptop to use a static IP would be the easiest. As long as the laptop is running and RDP service is available, you would connect local IP to say 192.168.1.12 if his static IP is 192.168.1.12. This requires static entries for the subnet mask and gateway for the network that its connected to.
Re-reading what you have, you say your XP computer is slow and want to connect to your brothers laptop remotely. So you want to experience the speed of his computer and have your Windows XP computer act like 8.1 maybe through a remote session to his system in which stuff is more responsive possibly. But the only catch is that that laptop will only allow 1 person at a time to use it. So If he is using his laptop, you wont be able to have a session open on his system at the same time. It will lock his computer on him when you have remote desktop access. Additionally Multimedia and Video Games are horrible and some down even work through RDP. You would be able to surf the web, download stuff to his system and not your own, and make changes at his system to local files and thats about it.