Just start problem? Not that it started, droved and died then you had to wait some hours or whole night and then it started again?
It’s tricky on newer cars.
Have you checked the diagnostic system? Small little black box next to the hood hinge on the driver side. It will blink some Morse code and inform you about errors in the main system.
It could be a trigger inside the distributor which is tricky to remove since it’s between the engines and body (tight), this can cause bad timing on the sparkplugs. An electric man can test it without removing it; I don’t know how they test it but…
It could be the air mass calculator (probably called something else in English) a electronic box between the hose and the air filter box, unplug the electric cable = engine will drive on a standard setting, but having an failing box plugged in would mess it up.
Do the fuel pumps (two, one under the driver seat, under car) sound anything when you turn the key one step? It can pump fuel but perhaps not give enough pressure with just one working pump. Or time to change the fuel-filter.
Perhaps bad compression inside the engine? Don’t think so but it’s easy to check. Have you checked that the timing-strap is okay? Well this should made the car stop directly not be worse and worse.
Water in the gas tank? I don’t know you current weather condition. Not that they should be so sensitive for that.
Could be a relay, for the injection, gas pumps, or something… Not so many, 2-3, but it isn’t fun job to find out.
Start to run the diagnostic system and see if the car will tell you the problem…
Good luck..
(780 and 740 have slightly different bodies so it’s actually the wrong category we are in now.)