I pulled the glove box, pulled the rubber cover off the blower motor, and removed the blower motor. I found quite a bit of water in the plastic housing where the motor goes. You can see the water at the bottom of the circular housing:
A close-up also shows moisture through the circular hole. I assume that's where air comes into the blower?
I could not figure out where the water is coming from. Everything above and around the blower appeared dry. No evidence of a leak. I even pulled the cover of the air intake (in front of the windshield, where the wipers are) and poured water into it. It appeared all the water drained under the car; no evidence of any of that water making its way to the blower.
By the way, the blower works on the highest fan setting. Nothing on any of the lower settings. I guess that's something else to deal with.
Since the problem no longer seems to be an issue of pulling the dash, I'm going to repost much of this into a new thread with a different subject heading.
Thanks for the input,