Tesarect
Our family had similar problems. We'd all be online, then one computer would get on (it was generally our multimedia computer), and everyone would be disconnected. The thing that worked best for us was to buy a more powerful router than could handle more computers. My problem doesn't sound exactly like yours, but that's what we did. We ended up buying a small business class router, since we have so many laptops and smartphones/iPods and stuff.
This would be our alternative, but Considering how old the router is (Yes, it's a 2Wire, claimed by one of my siblings its VERY old.) and the Speed it has is just 70ish KB per second...
I am suspecting that computer is using High bandiwidth, but its a legal Assume.