Sounds like you might have an engine breathing problem which could be caused by an intake/exhaust restriction or an EGR leak. Probably the easiest thing to try would be remove the upstream O2 sensor from the exhaust. If the exhaust is blocked (plugged cat), removing the sensor will give the exhaust gasses an escape route which might allow the engine to run.
If Hyundai cars in NZ have transponder key immobilizers you might want to try using the spare key to start the engine. The engine starting and immediately cutting out can be a symptom of an immobilizer issue too, but the engine doesn't usually run as long as 3-4 secs. Still, quick and simple so maybe worth a try if you have a spare key.