Sometimes I'm a dolt. My concerns about the state of my eReader were premature and unfounded. Turns out that when the device's battery has been sapped, charging via USB isn't enough to get it back up to snuff.
Since my chat with the service rep, I've dug out the AC power adaptor, plugged it into my kitchen counter socket, and away we go. The eReader is working like a charm. Thankfully, I didn't send it in for repair. The repair folk would have had a laugh!
Now, if only I could get my Thinkpad's cup holder to work!