In case you haven't sorted your problem out yet, I will still offer my input. And if you have worked it out, still interested to know what it ended up being if you don't mind updating.
Definitely sounds immobilizer related. If you need a new key, I would get that first and then you can rule that out as a suspect. You can check to make sure none of the buttons are stuck down though in the mean time. If for example the lock key is stuck and being constantly pressed, it will reengage the immobilizer non-stop and all you will get is the motor turning a few times and then cutting off. It will also stop your key unlocking it, the door locks will not operate while a key is pressed on the remote, when this happened to my father he was in the car and couldn't even physically lift the lock from the inside, also the remote wouldn't unlock it and he rang me while held prisoner by his own car. Sure enough a button had failed to click back out on his remote last it was pressed, and a little fingernail prying down the side of the button and everything worked fine again. You could try removing the blade from the remote and try unlocking it while the remote is well and truly out of range of the car. Or try pressing the buttons while paying attention to see if they are clicking back out. First test is more effort but also more definitive.
Your local auto shop will be able to provide you with a blank key blade and remote setup, as well as a little dongle you can plug on under the dash to code the new key to work on your car.
https://www.supercheapauto.com.au/p...-3-button-kf204/370799.html?bvstate=pg:2/ct:r
https://www.supercheapauto.com.au/p/map-map-key-programming-tool---suits-holden-commodore-vs-vz-kf200/370798.html#q=key+program&lang=en_AU
Don't bother paying to get the blank key blade cut, just unscrew your old one from the broken key and fit it to the new setup. Then you just plug the dongle in, turn to ignition and when the light on the dongle stops flashing, remove the key and then dongle and you're done. The coder is good for coding 3 keys with so its a good time to make any extras for other drivers or a spare if need because while the first one costs you about $140, the other 2 are about $60. Last time I actually bought the 2 extra blank remotes and put on gumtree $120 for a programmed key. Before long 2 people had messaged and stopped by and I just did the same process for them. My key ended up costing me about $20 after that from memory. That's a way cheaper option if you don't have a working key, but if you only want one key and can provide a currently working one to a locksmith, a freshly cut blade on a brand new programmed remote should only cost you about $100 from a locksmith kiosk at the shopping center and can be made while you do your shopping. But last check a fully equipped locksmith shop and about $400 was required if you had no working key to start with, then you will benefit the most from programming your own.
I'd be very surprised if that doesn't sort it out, but keep us updated. If you skip the first bit and go right for the new key, just make sure the old one is away from the car while doing the new key, as you won't know if its spamming signals, and it may make your new key appear not to work. Hopefully though, you just cleaned a bit of gunk out from the side of your button remote and are already off for a drive. Hope this helps you, or someone with similar issues.
