By reconnecting the battery you may have triggered the alarm system.
You alarm my have immobilized the engine. If this is a Toyota installed alarm try locking the car and opening it with a key.
If you have the type of key with the chip inside try starting it with this key, try both gray and black key if you have them.
If you have some kind of aftermarket alarm try the following: Look under the dash for a button or switch. If there is one try the following: Turn ign key on to the position before engine crank. Within 5 seconds press and hold in the override button until the LED (the blinking light) in your dash area goes solid and the siren chirps once.
If there is a toggle switch instead of button repeat the process but turn the switch in opposite direction then turn ignition switch off.
Many after market alarms are installed into the ignition switch Remove the cover under the steering column and look at the wiring to the ign switch area to see if something was added.
Removing the fuses this alarm should disable the system. If the alarm was wired in the typical way the starter kill circuit is wired in a normally closed configuration and the car should start.
If alarm was wired in a normally open method find the starter wire (red wire in the 98 Camry) and reconnect it to the ignition switch wiring.
If the car has a remote try the site below to determine the vendor and thus be able to contact them for instructions.
Next time you change the battery if possbile keep power to the battery terminals via a small secondary wire.