Was the old battery dead, if so did you just attempt to start the car and find it dead. Did you try jumping the car to get it started?
The fuses can be in series and then branch off. Often a series of parallel fuses come of a single source of power. See if the blown fuses have anything in common such as their power source (other then the battery of course). Perhaps something in a circuit overloaded, blowing out all the fuses in this circuit.
Hard to imagine all the fuses blowing, check each one with an ohmmeter. You would be better off finding a wiring diagram to give you an idea of the circuits.
Below is a link to Camry service info. Not the same as your model but may be close enough to help you.
http://oregonstate.edu/~tongt/camry