Two computers one modem D:

Sup folks, Im really at a loss for whats going wrong here... Ive got two computers one is currently connected to the internet via a modem the other is not... "Thomson Speedtouch 530" is the modem, Its got one ethernet port on it. Simple works fine. Now up till this morning my second computer could connect to the net I would normally just flick out the ethernet cable of this computer and pop its one in. Give it a minute to figure out its there and it would connect. It died this morning it was pretty shod in the first place but I ripped out my sisters old computer gave it more ram new graphics card and my sisters harddrive. It turned on much quicker this round but I cant connect it to the internet like i used to. I plug it in and it doesnt do anything. My sister had a wireless internet connection on it which I no longer have and I have tried to set up a connection but nothings doing nothing. Both computers have windows XP. I need them to go threw the same modem so is that possible and if so how do i get it to work? Any help would be muchly appreciated :)