Searching around on the web to see if the flashing lights meant anything, I came across this page. It seems like lots of people have been reporting the same symptoms: just after the warranty expires, the battery mysteriously "dies". Even the Dell forums are replete with posts from unhappy users.
The solution from Dell is: buy a new battery. But they aren't cheap: a Dell one runs you about $100.
I know I should have known better than buying a Dell (cue the "Dude!" jokes). But this begs a bigger question: is this legal (it certainly doesn't seem ethical)? How many of these (working) batteries end up in the landfill? Have laptop batteries become the next "printer ink", forcing us to keep buying new ones?