The early '01 models had some trouble with water in the interior fusebox, located in the driver-side kick panel. If you remove the fusebox cover and see any rust stains, take it to the dealer. If you're handy with electrical work, you could also disconnect the battery and remove the fusebox to see if there are any water-induced shorts.
You may also have an Accessory Delay relay that's stuck in the closed postion. If your power windows still operate, even 20 minutes after you remove the key from the ignition, this is probably the problem. This relay is located on the back side of the interior fusebox (location C2075).