Having 2 cilinders open, causes the engine to have less resistance in idling, could be why it is idling with 2 cilinders and not 4. If the car has been standing still for a very long time, the connectors could be corroded.

Firtst my money would be on the electrical system, corrosion due to long storage.
Try cleaning the connectors to the coils with contact spray, and with a small screwdriver scratch the surface to remove any corrosion where possible,
Also the connectors furhter down the line, if there are any, and even remove the large connector from the ECU and clean with contact spray. (remove battery lead first).
Also the ground wires connection to engine and chassis might be subject to corrosion, as wel as the connectors for the plus wires. And the battery could still be the problem, after sitting for a few years it may have lost capacity, or have an internal defect. Also clean the battery + and - poles and clamps, caused a problem with my car after winter storage.
I have also had broken wires on a few old cars, the insulation was flexible original, but turns stiff during the years, which can even lead to wire breach. Nasty fault to find, most probable in the area of the engine that is vibrating and the engine heat causes insultation to harden, a combination causing wire breach in old cars.

The ultimate test would be to check the voltage on the coils when starting and idling on 2 cilinders, but that may be difficult because it has pulses instead of constant power, you need a scope, a garage will have that, and you need to be able to test the wires to the coils while in operations, you so cannot measure at the connector, probably need to remove a small piece wire insulation to connect the measuring probe.

Next would be to check the sensor readings, the ECU uses readings from temperature and MAF, and TDC, and REV to calculate the fuel mixture. You would need an advanced ODBII diagnose reader, to read the values. TDC and REV will probably be ok, MAF and TEMP are sensors that can fail. There are I think 2 TEMP sensors, one for cooling liquid temp and one for air temp.
If the ECU thinks the car is at operating temp, while it is not, or vice versa, it will give a wrong fuel mixture that may cause the engine to stall.
Also here, first check and clean the sensor connectors for corrosion.

If electrical there is no fault, next would be the fuel system. Check the fuel pressure, of course drain the fuel that has been in the car for a few years while in storage, put in new fuel, mount a new fuel filter. Pressure may be ok, but perhaps the fuel flow is not, may be a blockage of some debree somewhere. Although at idling you would not need that much fuel, so I would just leave it at fresh fuel and fresh fuel filter. You could have the injectors tested, but would not be my first solution, but cleaning the electrical connectors on the injectors is a good idea. One step further would be to remove the injectors and clean them with injector cleaner.
And just the same as the coils, a garage can check the injector voltage and pulses.

If the easy approach in the above give no solution, time to check the compression on the cylinders.
If the engine has a compression leak caused by a broken piston ring or a stuck valve, it will not run easily. But given the fact that it will run on cylinder 1/4 and 2/3 I would not suspect this.

Running fine and then stopping suddenly without any signs, indicates something has suddenly broken, perhaps due to the heat.
Having issues in electrical steering pulses to the injectors or coils, may also find its cause in the ECU itself, the electrical components are subject to aging, and don't like heat. The only way to check it to swap the ECU in a garage with another car, but I think the ECU is paired to the key, and perhaps even to the instrument panel, but I am not sure. So not a matter of just swapping I think, you need a garage to perform this test I think.

Good luck in finding a solution

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