Ethernet adapter for OLD computer

Sorry to create a new topic, but this is a different question to my other..

I've just had a look around and found this http://www.play.com/PC/PCs/4-/3516190/USB-To-RJ45-LAN-Ethernet-Network-Adapter/Product.html on play.com.

My old computer hasn't got an ethernet plug socket thing for the cable from my new Wireless router/modem, would it be possible just to plug the router into the old computer using this thing?

Also, I'm running Windows ME on the old computer and the Tiscali CD says it won't run on that, it needs XP or Vista. Is it possible to install the broadband onto that computer without the need for the CD or an upgrade to Vista/XP? Just thought it seems silly seen as people must've been using broadband in the past without the need for XP or Vista....

Double also, do I need some kind of network card for the old computer to be able to run that on wired broadband AND run my laptop on wireless from the same router?