This thread seems similar. And a couple of other web sites seem to report the same problem - if the Kindle battery discharges too far, it won't charge, because it's not got enough power for the charging circuitry, or something.
Several people have reported success by plugging/unplugging or turning on with the switch, to get the orange charging light, many times to get a little charge in each time, until it finally has enough to start charging normally.