I broke down and called Dell today. The tech was actually very nice, and I didn't have to argue my way into a new battery deal. It took an hour on the phone (including hold time), and I had to repeat steps I'd already done before calling, but... They are sending me a new battery! It should be here in 2-3 days.
I could only find one other site that has documented this problem: http://kniffen.ca/2007/01/19/dell-laptop-battery-bs/
It sounds like we have a new dell battery issue here. If any of you experience similar problems, I encourage you to post comments here, or at least post a link to your own site or similar sites. I would like to make an effort to get the word out about this new battery problem. This may be the start of yet another Dell battery recall.
Call Dell and get a new battery!