Your vehicle doesn’t have an alternator but instead has a generator. The voltage regulation to the battery is controlled thru the ECU or the computer. Here’s a wiring diagram of your charging system. http://www.scribd.com/doc/12962382/Scion-xB-2005-Overall-wiring-diagram
The computer may have failed where it’s no longer allowing the battery to be charged from the generator. However, the computer in your vehicle is covered under the manufacturer warranty for 8 years/80,000 miles. So if the computer is the problem, and you fall within the warranty period the computer should be replaced by dealer for free.
Tester