Have Toyota Questions? Ask a Mechanic for Answers ASAP
Does anything illuminate on the instrument panel when the key is turned to the on position? Does it crank over and not start or are you getting no starter engagement? At any time was the battery installed backwards or was it jumped backwards?
Does the neutral indicator light up and did you try and start it in neutral? Did it start perfectly fine prior to the battery replacement?
Do you have a simple 12 V test light or voltmeter to check for voltage on the engagement wire or the small wire going to the starter? Can you hear the starter relay clicking on or the starter solenoid trying to engage? The park indicator light is not an issue at this point it should still start in neutral if the transmission is shifting in the neutral and the light is coming on.
Without at least a simple 12 V test light is going to be difficult to get you to a definitive resolution. If the starter relay is not clicking we need to check for voltage at the relay and continue from there. It's possible it's just that the starter itself is stuck because it hasn't been started for a couple of months. Is this something you will be able to acquire a local parts store?
It is not necessary to buy starter just yet we need to confirm whether or not you have 12 V going to it I was asking you if you could get a simple 12 V test light and check to see if you getting 12 V there. The Starter relay is located in the fuse block under the hood inside the lid of the fuse block it will give you a description and layout you're looking for the STA relay.
Using a simple 12 V test light is very easy. You don't need a fancy power probe just a simple clamp on one and a probe on the other end with a lightbulb in the handle. Clamp the one end of the test light to a good clean ground on the engine or intake manifold then there will be two wires going to the starter. Small wire is the solenoid wire carefully back probe that wire or disconnected from the starter and probe the female pin without damaging it and have someone turn the key to the start position if the test light illuminates then your circuitry is good and the starter is bad. If you turn the key to start position and the relay is not coming is possible that the relay is bad .