Windows 7: Router reversed

Is it possible to get a router (by that I mean buy one) which basically gets the Internet connection through wireless, and gives it to a bunch of old computers with no wireless card through Ethernet?

What your talking about is a network bridge or access point, the two modes are different. You would need a regular router and an AP/bridge set to bridge mode.

The one I'm using is a Dlink DAP1522 which I'm using in AP mode, highly recommended.

In bridge mode it will connect wirelessly to a router and has eithernet ports so you can connect other machines to it with a standard eithernet cable.

In AP mode you need to connect an eithernet cable to a wired switch which would provide an access point for other wireless machines to connect too.

You could also get a linksys modem/wireless router. That will solve the wireless internet to the router. It's like combining a modem and a wireless router. But sadly you have to get rid of your old service provider.

Already got a wireless modem router.
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The problem is that the only working wall socket is on the other side of the house, so I have to use wireless to my room. I believe I have a spare router, so is what you're saying that I need an access point?

If you already have the router/modem you can have wirless to any PC or LAPTOP with a wirelesscard. Otherwise, if you don't want to drag all your desktops to the other side of the house where your modem is, then you probably need an access point. Buy it from your prefered network gear provider. Set it to bridge mode (More explination by chev65 3 posts to top) and you can connect your desktops through ETHERNET.