Long wait for a reply but here goes...
If you want to run a cable you have a couple of options, first you could just connect the two machines with crossover Cat5 cable. This will allow you to share files and folders and using Internet connection sharing you be able to share the Wanadoo connection. The upstairs machine will however only be able to share the connection if the downstairs machine is switched on as the downstairs connection acts as a gateway to the outside world.
If you were to get a router then the downstairs machine can be switched off as the router is then the gateway. You can go hard wired on this if you want by plugging the Wanadoo connection you have now into the router, the upstairs machine will also plug in to the same router.
Even easier and a cheap option is to get a WIFI router and a USB WIFI adapter, check out Ebay or search online for one. You will see they are named 812.11[letter] the one ending in "G" is the fastest but "B" would more than likely be enough for you.
Its a doddle to set up and again you don't have to have one machine on for the other to work, WIFI will be a lot easier and less messy to set up. click here for a selection of routers and click here for a choice of USB WIFI adapters.
Hope all that was worth waiting for.