2005 TS Yaris fuel pump?

[TS Turbo]

Hi!

First post on this forum so hello to you all :)

I have a 2005 Yaris TS Turbo. This is as far as I know the European version of the Vitz. ***might be wrong here as you see further down***

During the really cold winter here in Norway my fuel pump died. So I was wondering if anyone knows if it is the same fuel pump in a TS turbo as in a Vitz? I have tried searching for this but it is quite hard to figure out. The engine code for my car is 1NZ-FTE and for a Vitz it is 1NZ-FT. The E at the end might just be "Europe" but I don't really know.

Does anyone know the difference between them, if any at all? Maybe even know what pump fits the TS turbo? Is the pump labelled so I can just take it out and search for it perhaps? Any tips is appreciated :)

And just for fun - is it possible to fit a more powerful pump and get a benefit without more modifications to accommodate the increased fuel flow?

Edit: Should probably add my diagnosis:

-The car had been sitting for several months in 0 degree fahrenheit/-20 celsius weather.
-The tank was 3 quarters full
-Battery was completely dead
-Hooked up another good battery
-Car cranks strong but no sign of detonation
-Can't hear hum of pump when turning on ignition, but can hear the relay click
-Checked a spark plug and it was dry even after a lot of cranking

After looking at pictures of the Vitz I'm not sure they are the same car at all - This is how mine looks