your computer sucks -- can't help you there
your intenet conenction sucks -- can't help you there
your ports are not set up correctly -- can help you here.
go into your router (usually just by going to 192.168.1.1 in IE/firefox). if you use a linksys router, you need to port-forward (under applications and gaming) ports 6881-6999, 90-91, 5000-5001. that will take care of all the popular trackers.
also, if yo'ure on xp sp2, with the winblows firewall turned on, you will need to "add a port" for 6881, on both udp and tcp, as well as 90 for both. you can get to that via the my network places.