Engine immobiliser won't reset and allow the vehicle to start

check the battery in the key as the engine immobiliser may not be able to read the unit and assumes that you are trying to steal the car. It will allow all that you have said but will not allow the cpu to allow ignition and spark

Disconnect battery and let it sit overnight.

With the engine off and cold, open the hood and locate the vehicle's radiator and water pump. Remove the radiator cap.Install a pressure tester on the radiator. Apply the pressure indicated on the radiator cap or in the owner's manual. Inspect the water pump for leaks. Remove the pressure tester. Place a drain pan under the radiator. Open the drain valve or remove the lower radiator hose to drain the cooling system.-----------------------------------------------------------------------------------
CARPROG FULL V4.01

run the scanner to reset the ECM and immobiliser
make sure that the cranking speed is fast
check for air in the system
check that the stop solenoid is connected

Replace the battery in the remote.

Hello Jaclyn... Your Camry has an "engine immobilizer" designed to prevent "hot-wire" starting incorporated into the anti-theft system...This was standard on the XLE, & an available option on the LE. When the battery cable came off the immobilizer lost it's memory & is not reckoning the chip in the key. Try locking and closing all the doors. Then unlock the drivers door with the key. Repeat this several times, also tap the brake & gas pedal. If this does not help the dealer will have to reset it by the vehicles VIN number.
I hope this information is helpful.

The 'Keyless Entry & Burglar Alarm System" is activated. You must 'Disarm' the system using the Keyless Entry Remove (Key Fob) to "Reset" the system. The reason the engine won't start is due to the burglar alarm - it has a "Starter Kill" circuit which is activated when the alarm is activated. The alarm must be DEactivated to DEactivate the 'Starter Kill' circuit.
Another way to start the engine is to get in the car, put the key in the ignition and turn it to 'ON" and wait 3 to 5 minutes until the emergency flashers stop/turn off. Afterward, you should be able to start the engine. NOTE: This does NOT reset the burglar alarm. It will go off again when you enter the vehicle without using the remote/key fob.

I would troubleshoot the wiring and all ground points to eliminate that. Then swap out the ECM to see if is defective.

is it the original key? if it is a new key that you have cut & your vehicle has a factory engine immobiliser that can be a problem if the key is not a genuine buick key, reason being the key has a transponder incorporated in it which activates & deactivates the immobiliser & without that the engine wont start, the key will open the doors ,activate the starter & nothing else......hope this helps.......cheers