Also on my hp the hardware was installed but the drivers weren't installed for the wireless card, make sure you don't have a floppy or a cd that came with the laptop with the drivers on it.
Also cedar when I got my Lynksis router, it wouldn't work (because of the driver problem) but I called lynksis and they were very helpful. Good customer service with them.
To start answering some questions...since under Network Connections it does show a Wireless Network (though it's not connected), that leads me to believe the adapter is wireless-capable.
I bought this laptop at radio shack, and the salesman sold me the router too --- he was pretty much a techie, so surely he would have mentioned no capability if there wasn't any. I asked him specifically what I needed for wireless, and he said all I needed was the wireless router.
As for the drivers, I do have the driver recovery DVD -- it says it contains drivers that are already installed on the laptop, and is for recovery only.
Since I am getting regular internet connection (just not the wireless connection), seems like the driver must be functioning. Plus when I ran the router software at the beginning, it said I needed to download an update, which I did. That download was from Broadcom (which handles the wireless part, I think)... so it seems I have all necessary driver updates.