Toyota Repair: car not turning on, toyota camry 2002, toyota camry

Question
Hi Ted, i have a toyota camry 2002 with 171k miles. the last 3 days it is giving me problem when try to turn it on.  i noticed it took more time to turn it on.  today, i try to turn it on and it crank but didnt turn on. then i put the key to off position and try again and it turns on.  i went to my destination but when i was ready to go home, the car didnt turn on.  there is no crank. the headlights turn on fully so i know it is not the battery.  i tried giving it a boost just in case but no luck.  when i try to turn it on, i dont hear a click sound either so i am assuming is not the starter either.  when the starter goes bad, you hear a click sound.  the lights in dashboard are on but there is no crack and the click sound.  it is like you have a dead battery and you try to turn on the car and there is no crank and no sound.  so i am ruling out the battery because it works. dont think is the starter.  i am thinking it could be an electronic part.

do you have any idea what could be the problem? thanks for your time.

Answer
It could be a problem with the neutral start switch, try moving the shift lever through the gears while trying to start it ending in either park or neutral, possibly bad contacts in the switch. If not look under the hood in the large fuse box near the battery and find the starter relay, the relays are marked inside the cover, ig not there look in one of the other smaller relay blocks, if it has the starter relay swap it with another relay that fits they are mostly all the same as long as they have the same connector configuration.