WOW thats pretty cool, looks like exactly what you need. I can't guess how eary or hard it is to configure and you may need to add a wireless card to the desktop (maybe not...)
For everyone else looking, here is a link http://www.alwaysonwireless.com/wiflyer.html
FYI your ethernet is commonly called a NIC, LAN, or 10/100 card.
A cross-over cable is normally a Cat 5 cable with pins 1-3 and 2-6 crossed over. It is used to connect two pc's without a hub, or in this case a pc and a wireless access point.
An access point just serves as wireless media, think of it as a piece of cable that a bunch of pc's can hook to. The router you have has alot of intelligence built into it, can be confusing to people who don't do much networking.
I say send back the router you have and try the wiflyer. Worst case you will have to send it back and drop another post here and I/anyone can help you with the hook up and settings.
If it works the wiflyer would be a much cleaner approach to your problem.
I think I am posting at least three cents here... sorry about that. Good luck!