Check the firewall settings.  By default the Windows firewall would allow the connection.  Is there some third party firewall running?  If so, shut it down and then check.

you've mentioned that:
"In the Network Connections screen, it's listed as "not connected, firewalled."

meaning its not configured properly... all you just need to do is make sure your wireless zero configuration says STARTED and NOT STOPPED. then you can scan wireless network back again and connect to it....

go to services.msc then look for WZC so you can check if its started or stopped...

I reset the firewall back to the basic settings and I'm only using the Windows firewall. Also, given that my PCI test won't start I think it's that the hardware isn't turning on... but it sees the hardware... hmmm.

I checked the WZC and it's listed as "started, automatic"

There were a few that were disabled. Do you think any of these are the culprit?

Network DDE

Network DDE DSDM

and Routing and Remote Access

If any of these are my evil little nemesis, where do I go to restart them? Could this be a virus flipping my switches?

Thanks everyone. I have a little hope now. I have a hammer nearby just in case...

try using an eth cable first then check if you can surf to the internet on normal mode, if not goto safemode with networking....

if still doesnt help try going back to normal mode open a cmd prompt type this commands...

netsh int ip reset filename.txt then enter

and

netsh winsock reset

then try using both wireless and eth connection...  

OK, so perhaps it doesn't "technically" count as the solution. I did try all the safemode stuff and it didn't work... but... I started thinking about your "workable BIOS" tag...

Somehow, wireless had been turned off in the BIOS. Everything's great now, THANKS!