At this point it looks like the following fix has solved the problem, and as a good cyber citizen I've posted it to help others.
I re-seated my new wireless PCI card. I had to push it in a little harder than I normally do (and a little more than I was comfortable with) to feel it "pop" into the slot. I also put it into a different slot.
For those new to computing, "re-seating" a card means taking it out of the PCI slot and pushing it back in.
What tipped me off was that it also froze in Ubuntu (I set up my system as a W7/Ubuntu 9.04 dual boot), so I figured that it must be a hardware issue, and my rig was running perfectly until I installed the card a few days ago.