Your post is really confusing...but I think I understood most of it...
Firstly, no, most routers do not have an integrated modem, yours being no exception (I checked). Secondly, the magic of wifi is that you can have the wireless router all the way down in the basement with your modem, and still connect to the internet from your computer upstairs. I'm not quite sure what problem you are having, but all you need to do is buy a PCI WiFi card for your computer (about $50), plug your ADSL modem into your router, and you're good to go.
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