1999 Intrigue Randomly Won't Start

My car randomly won't start. I'll turn the key, the lights will work, the radio
works, but does not start. The battery, alternator and starter are all new.
Sometimes if I let the car sit for a few hours it will start. Then it will start fine
for a few days then won't start again. I've even had the Neutral safety switch
replaced. What other reason could make the car not start like this?

Does it crank at all or make any noises when you try to start it

no. doesn't crank. no noise at all.

and now it won't start at all. it's been dead since this morning.

If the security system is in lockout, leave the key ON for 10 minutes and it should enable the system to start.

my security light is not on when I leave it in the on position.

Put a volt meter on your starter ( small wire) have someone crank and see if you get voltage if yes it's a bad starter. If no trace it back and check at the starter relay.

I agree with harleyguy......

If you turn your key to on, only, should see the SECURITY light come on for 3-5 seconds and go out.....if it does, then turn key to crank...

If nothing happens, try starting in neutral....if still nothing, check for power at the purple wire to the "S" terminal of the starter solenoid.....if you have power, bad starter.....no power, there is a crank relay, in the underhood junction block....do you feel it click when someone turns the key to the crank position? If no, try swapping the relay out, and try again....still nothing, check for power to the relay.....if you have power and no click, the PCM is either not grounding the relay, or there is a wiring problem in that circuit....