PT CRUISER 2002 AUTOMATIC DOESNT CHANGE TO GEAR 3

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This is the classic symptom of a failed reverse clutch pack, sorry you will need an overhaul.

(From ptcruzer.com: http://www.ptcruizer.com/computer-codes.html )
The 605 code may be a possible glitch in the computer's ROM (Read-Only Memory). To try and clear it, disconnect the battery, cycle the ignition a couple times , and also hit your brake pedal That will drain any residual power left in the system. Reconnect the battery after about 5 minutes, and start the car. Let it run for a bit, shut it off and then pull codes again.

The 700 code may be transmission-related. This might be a glitch too, but look for any other codes after you get past the first 2.

po700 is the code for the transmission control module. it is located in the front of the transmission. you can change it yourself

Hello, guys, you may read about this article. Why check engine light is on. It has a very detailed explanation why check engine light is on and how to solve the question.

I MEANS YOU ARE OVERHEATING MAKE SURE YOU HAVE ENOUGH ANTIFREEZE AND MAKE SURE YOU COOLING FAN IS WORKING I HAD A PROBLEM WITH 2 PT CRUISERS IT WAS THE WIRING GOING TO THE COOLING FAN IN FRONT OF THE RADIATOR TO CKECK THE FAN PUT YOUR AC ON THE FAN SHOULD AUTOMATICALLY COME ON IF IT DONT YOUR PROBLEM IS IN THE FAN

It means that your input and output shaft speed sensors see an error in the 2nd 3rd and 4th gear final drive ratios during the driving of the vehicle.

It is very possible that the transmission is going out. Need a little more clarification on what the codes mean that are coming up.You can go to Autozone and they can bring up the codes, and then they will tell you what those codes mean. It doesnt cost anything and could possibly be a cheap, quick, and easy fix.

Have a look at this:

http://www.obd-codes.com/trouble_codes/

This doesnt show up for your car and I was wondering if you could either cofirm it with him or get someone else with adifferent brand OBD 2 scanner to pull codes. Is your PT from europe?