Before you buy anything, I'd suggest you double check the basic networking and port forwarding stuff one more time. If the laptop can wirelessly surf the web, then it has a good connection, and replacing the router shouldn't be necessary.
Are your network devices within the house DHCP? Sometimes that makes for a moving target. With DHCP the router hands out ip addresses when computers ask for them, but there is no easy way to make sure you get the same address every time. When you set up port forwarding, if your laptop is 192.168.1.3, and then you reboot everything and next time it is 192.168.1.4, that won't work. The standard solution is to use static addresses.
If the desktop listens for torrents on port 6181 (I think that's a typical one), then the laptop can't listen on the same port. Jump to another whole range, not just 6182, go with something completely different like 14152. So one range points to the desktop and one range points to the laptop. Obviously in the torrent client settings they have to match those addresses.
If you do that, and that doesn't work, then I would do the following (some geek factor required)... this will test of the laptop is listening on the listening port you think it is. Open a shell on the desktop and type "telnet <laptop address> <laptop's torrent listening port>" like "telnet 192.168.1.4 49152". If you get something like "connection refused" you still have a bad setting on the laptop because the laptop is refusing the connection that a torrent would try. If it connects for a little while and then goes away, then I would say the laptop is fine.