I had a similar problem a while ago, with a different Wifi adapter. I solved this by temporarily going with an ethernet connection to the router in order to download the proper Wifi driver in Linux. But this doesn't seem to be an option for you, so it looks like your three best methods would be, ordered by my personal preference:
a) Download the (Linux!) driver (*) while having Windows booted, shove it onto an USB stick (That's what you meant by 'key', right?), then change into Linux, re-insert the stick and copy it off from there. Be sure to have your USB-Stick formatted in a way that both OSes can access it (FAT should be fine for that). Install the Wifi driver in Linux.
b) Download the (Linux!) driver (*) while having Windows booted, then re-boot into Linux and mount the windows HD partition into your Linux file tree. For more help on this, see, for example, this link.
Copy the driver over to the native Linux environment, then install.
c) A 3rd, if somewhat similar, method would be to just use the cell phone to download the (Linux!) driver (*). Assuming you've got an USB connection working in your Ubuntu, just connect the mobile phone to the Desktop via USB cable, copy the driver over and proceed like usual.
(*) A quick look-up confirmed the driver seems to be easy to find and to download. However, that quick look-up didn't show me the manufacturer's page, so I refrain from putting a link in here.