The very first thing that you need to do is to personalize the wireless settings of your ultra range plus router. Since your laptop is wired directlty to the router and is working properly, you can access the router's GUI to personalize the wireless settings. Open internet explorer on the working computer and type http://192.168.1.1
on the address bar, you will be prompted to enter a username and password, by default there is no username and the password is "admin" if you have setup a password using the setup cd then use that one.
Now your inside the setup page of your wireless router, look for the tab the say's Wireless and below you will find four sub menu namely; Basic Wireless Settings, Wireless Security, Wireless Mac Address and Advance Wireless Settings.
Under Basic wireless settings change the Wireless Network Name(SSID) to something you prefer(this is a must).
For the Radio Band, set to Wide 40Mhz. Wide Channel(9), Standard Channel(11) now click on "Save Settings".
Now got to Wireless Security and for the Mode choose(WPA Personal/PSK Personal) Enter a 8 or more digit password under passphrase and click "Save Settings".
Now your done setting up your wireless router it's now time to connect your desktop wirelessly.
If your using a linksys wireless usb network adapter more or less you have also installed the WLAN Uiltility but personally I use the built in WLAN of XP and Vista.
Using the linksys WLAN Utility for to the Profiles tab and highlight default.
Click Edit and it will provide a list of available network(SSID) that your computer detects.
Select the name(SSID) that you provided the router earlier and click connect.
It will not prompt you to enter the WPA Key also known as passphrase(remember the 8 or more digit password) then click Connect to the Network.
You should now have a valid internet connection wirelessly on your desktop.
Oh and for your 2nd question the answer is No, since you already purchased and installed a wireless usb network adapter for the desktop computer you don't need to purchase a long ethernet cable or move the desktop to where the route is.
Hope this will help you get connected.