2003 Pontiac Aztek wont turnover. Lights battery starter new, no sound from the starter Stuck in park too Then it starts Tow truck lets it down, and it starts, until later then it happens again.

REPLACE STARTER...

01 pontiac have chip in the key. If you key is removed wont start.The key send signal tho body computer, body computer confirm pass code to engine computer ,ecm send signal to safety neutral switch next is starter relay and last is the starter.some times transmission switch is not line up correctly.turn the switch to start and hold and with other hand move slowly from park to neutral.if your car start inspect the shifter links or the switch for correct alighment.

Have you Checked the Bulbs themselved?

Test the Sockets to ensure you are or are not getting power.

Once that is determined we can help you further

Used parts such as starters and altinators don't last. It might **** but it sounds like you need to buy a new starter,altinator, and battery. Or just start with buying one at a time.

Here's a video showing you how to remove battery. Battery Replacement 2001 2005 Pontiac Aztek 2003 Pontiac Aztek 3 4L V6

Sounds like you are right that the plugs are fouled out replace and fix your problem.

sounds like the ignition lock cylinder has gone bad call a locksmith.

Your problem is either the Alternator isent charging its 13.5 volts and the battery is flat or wont hold the charge SO do this.
Jump start engine again let it run for 2 minutes then turn on lights,, the head lights should go bright at 13.5 volts. it engine cuts out..and the lights dont go bright,, then the Alternator is not charging,,,, If they go bright and still cuts out the batterys NO GOOD.
Replace battery or get it checked outit must hold 12volts all the time Let me know how you get on.

YOUR PARK LAMP RELAY IS STUCK IN CLOSED POSITION.NEED TO REPLACE IT.

You will not get far with this without doing some testing. Check battery for 12v (lights draw far less than starter...,what appears as OK often is not) if battery is low, charge and load test it. Once verified as good you need to check that starter is getting voltage when key is turned to start.Check battery connections at both ends of main wires for clean/secure connections. Beyond that there are code tests and individual component tests outlined in most inexpensive manuals you can do with any decent digital volt/ohmeter (computer scan tool needed for code testing) Once started, use volt meter to check charging system.
Even if I was standing right there, I'd need to do testing...stuff costs way too much to guess your way through it. Good luck and feel free to ask if you have any specific questions.