Engine starts but shuts off after three minutes

That is not the passkey system. Passkey would only let it run two to three seconds. Start and run three minutes or so sounds like a fuel pump issue.

What does the security light do? Is it on when you try to start the car? Does it come on after the engine starts? The way that system works it will at best let the engine run for a couple seconds because it only runs the pump prime signal. If the system sees the wrong key or there is another problem the PCM is sent a fuel pump disable signal and the pump does not turn on, that means 99% of the time the engine will not even start.
What is the starting and running fuel pressure? What other problems are you having?
What do you have for scan tools or diagnostic equipment?

145 PSI or kPa? If psi you are way too high. 53-55 is normal. If kPa you are far too low in pressure, 372-375 kPa is normal.

Both ways will not allow it to run.

If you put the key in and turn it to the start position does the security light stay on while the engine turns over or does it go out?

Okay, if the light blinks and goes off when you try to start the engine the system is reading the key and recognizing it. So it isn't the pass-lock system.
If the light was staying on then it would be the passlock system.

Battery drained could be the root problem. If you have a bad battery and possibly a bad alternator it may be sending AC into the control system as soon as it starts spinning up and it scrambles the PCM.

You are losing spark or fuel when the engine stops running we need to see which.

Here are three guides designed to help us see which system is failing if the security light is not flashing chances are it is not a security issue.

https://www.2carpros.com/articles/how-to-test-an-ignition-system

If no spark is observed it sounds like a crankshaft angle sensor is going out.

This guide will give you an idea of what you are in for when doing he job.

https://www.2carpros.com/articles/crankshaft-angle-sensor-replacement

This guide may help as well

https://www.2carpros.com/articles/car-cranks-but-wont-start

Please let us know what you find out.

Cheers, Ken

Which one? Crank sensor or?

Nice work, we are here to help, please use 2CarPros anytime.

Cheers, Ken