Network Cable Question

My main pc is a Dell (Windows XP) and it's hooked directly my Linksys wireless router-firewall. My second computer, six year old Compaq running Windows Me 128 ram, is hooked up wirelessly to the router.

Ever since I hooked the Compaq wirelessly to the router the computer has had trouble keeping hooked up to the wireless signal. I'm sick and tired of messing with my second computer. I want it hooked up to the internet and I want to keep hooked up to the net. So, I'm thinking about taking out the wireless card and instead running a cable from my router to the second pc.

Here is my question: My main PC and router is in the corner of the living room. My second PC is in another room. What I want to do is run a cable outside, run it around the house, then run inside the room to the second PC, and then hook up the Compaq to my router. So, what kind of cable do I need for this long connection? A network cable? I want to run this cable outside the house. Can a network cable withstand cold-rain-snowing-freezing weather? Do they make network cables long enough to reach around the house or will I have to buy three or four cables and hook them together? Will I need some device to boost the signal from the router to the second PC?

How should I proceed?

Thanks!