MG TF 135 starts and runs on 2 cylinders but not 4

Is there any advance with this problem & if so how was it resolved?

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

Our friend has recommended contact cleaner, which is fine, however do use the proper stuff & NOT WD40!
WD40 is fine for the job it was designed for, which is for expelling moisture, it is not really a lubricant & it certainly is not a contact cleaner.
The chemicals in WD can destroy certain plastics & some electronics are made of those certain plastics. I have seen electronics destroyed by liberal amounts of the stuff.
Don’t let your electronics be amongst those.
M

If you've gone through all of the suggestions offered with no result, the cause could be a blocked exhaust, the media in the cat converter might've started to break up and some has lodged itself in the exhaust system partially blocking it.

I had this one happen to me with my Ford Falcon ute.
I had problems with the old girl running like a hairy goat and went though checking all the usual suspects to no avail....I then found a piece of catalytic media sitting on the driveway so I dug out my exhaust pressure test gauge (which is normally used to test to see if custom exhaust systems are an improvement, by measuring back pressure) and found the exhaust was almost completely choked, the guts of the cat converter had completely broken up, leaving it pretty well hollowed out and had moved downstream to block the muffler.
 

I would never have considered that in a month of Sundays & this fellow contributors is why Cobber’s contributions are so important.
Rather than start again I thought I’d edit this. A oscilloscope would be required to check the voltage, waveform perimeters etc, but you could get an idea of what’s going on by using a LED. A simple test rig of a LED & a series resistor (1k is a useful can do most value) on a couple of fly leads into the pair of coil feed wires & with the polarity correct you should see a flash when there’s a pulse 
M

Just in case it is affecting test results the correct firing order is 1 3 4 2. However I don’t think it’s possible to connect them incorrectly the coil pack wiring and plug lead ensures that you get it correctly connected. 

When researching “knock” on line it became apparent that two flame fronts reaching each other was one of the potential sources of knock. So I’m surprised that two sparks is a good idea?
How is that controlled to avoid knock?
I can potentially see that two sparks at the same time aiming to create a larger uniform spark would seem beneficial.

Alfa Romeo, and Nissan both produced production cars using 2 plugs per cyl with out any problems.
It's also used in some aircraft engines, and some racing engines in the old days.
These days cylinder heads lack the real estate to for 2 plugs as all the space is occupied by large multiple valves.

This could be wide of the mark but could it be fuel starvation- only enough fuel available to feed 2 injectors but not 4.

What happens when you try with 3 cylinders ?. Just 1 plug and lead removed

It’s great fun throwing ideas around as we have had no feedback from our questioner.
Any one of our ideas could have helped resolve the problem, without a further comment from our man, we’re playing blind man’s buff, searching for something that’s nowhere to be found.
If it’s sorted, let us know & let us know what overcame the problem.
M