On the 1994 Toyota Camry, the “rapid clicking” is a common, tell-tale sign of a battery that has less than 12v. The accessories like lights, radio, power windows, etc only require 9v to operate, whereas the Starter needs a full 12v (12.4v optimally) to crank the engine over. If you have access to a voltage meter, take a quick reading across the battery posts, I think you’ll find the voltage is well below 12v. I believe replacing the battery should solve the problem. After replacing the battery, you should have the Charging System (Alternator) tested to make sure it isn’t the root of the problem and not re-charging the battery fully. Most local “big chain” parts stores, like AutoZone, will run the Charging System test for FREE right in their parking lot.
Does your vehicle have a similar problem? Get connected to a Live Q&A session with a certified Auto Mechanic and get your answers on this problem now!