This really is going be a bit of a guess,,, give you the reasons why
The fuel pump will allow it to start, but then it dies, so though would like to say its the fuel pump,,, no real way of proving it....,The fuel pump could be getting switched off to save the cat, no spark, fuel pump is informed by the
to switch off,,,
Thats the fuel side, both give the same scenario...
Now holding the accelerator, this will hold
open, so this again should not be giving an issue,,( as regards being dirty),but running longer, but its still dying, this should disprove the first part of my statement about the fuelpump, but not the second part , being switched off by the
So thats pushing me away from a fuel/
Because it starts, each and every time, pushing me away from
sensor,, and because you can not keep it running, again, not pointing to a Engine Coolant temperature sensor,.
As you can force it to run longer, ..
So now we are on
, or fuse box, we will ignore
, because, if its gone open circuit inside, the heat generated very quickly, normally does not allow it to kick straight back in, but needs to cool down..
So it now points to fuse box,,,,
Would suggest, getting at the engine bay fusebox, take loads of pictures before you start taking it out, especially the route the wires fit, not on the fuse box, but how they are located, going to the fuse box...
Take your fuse box off the car,
See if you can see any sign of water damage, giving a poor connection..
Take a photo of how the fuses are fitted, now pull each fuse out and clean the contacts up,, Though its unlikely a dirty fuse will be the issue, but while its out have a look.
My thoughts are its your under bonnet fuse box, but just my thoughts,
But that would be what I would be going at, before I did anything else....