Ok back to basics (not teaching you to suck eggs btw)
Suck, Squeeze, Bang, Blow
Suck, have you got fuel & air entering the combustion chamber?
Squeeze, have you got correct compression
Bang, have you got ignition
Blow, have you got exhaust from the combustion chambers?
Running on easistart (startyabastid) would indicate no fuel, although it can have a negative effect in that engines get addicted to the lower combustion ratio, and become hard to run normally! (Although i would think it highly unlikly in this case )
When you turn on the ignition, does the fuel pump (run) prime and pressurise the system?
Battery fully charged 12.3V - 12.8V
Airfilter and associated piping not blocked, and inlets to the throttle bodys not restricted ( butterflys opening ok, not stuck open / shut)
Fuel at the injectors, and injector spray ok and at correct pressure.
Compression within acceptable limits
All spark plugs gaps correct and plugs sparking with a good blueish spark when tested?
Thats the simple stuff...
OK ignition sytems and cycles have made huge improvements / changes in recent years
The basic way to describe a generic ignition cycle is /was
Ignition on -
ECU energises and checks input values from relevant sensors
Cam / crank used to work out TDC and engine speed (needed for 3D ignition map)
Map / MAf - used to work out airflow into the engine, enables ECU to alter air / fuel ratio to maintain 14:1 ratio and Lambda ratio .97 - 1.03 (ish)
Lamda - measures fuel air ratio in exhaust and tells ecu its results so fuel air ratio can be adjusted - contrary to popular belief not all fuel gets burnt in the combustion chamber it ends up going out the back
Oil temp / water temp / Air temp all give the ECU inputs before ignition has taken place
Once all of that lot has fed its data back to the ECU and its all in spec (milliseconds)
The fuel pump will energise and pressurise the fuel system. - again an ok flag will be sent back to the ECU
ECU will have set the ignition map based on the data recieved earlier to give the
optimum fuel air ratio for the engine to start based on its current data (cold engine)
Pressing the starter the ECU looks for signals from
Injectors - Are they pumping fuel at the right time
MAf / MAP how much air is entering the combustion chamber
Crank & cam sensor - to provide spark at the correct times before TDC
Lambda - what is the ratio of unburnt fuel in the exhaust gasses
If ignition occurs, the ecu then looks for signals from the throttle position sensor /
or butterflys on the throttle body
Cam and crank sensor to work out RPM and ignition timing map
Lambda to work out fuel ratio
Oil / water temp to lean the mixture off as the engine warms up .
if all of the above are ok then the engine should be running normally.
In the old days you could have a misfire, and pump raw fuel through one or more
cylinders, and contaminate the cat and give the Lambda probe a real headache
Modern systems can detect lack of ignition, or ignition problems and shut down
relevant injectors etc to protect other systems down stream.
From what you describe, you have air, ignition and compression, but the fuel isnt
being injected, or injected at the right time.
That would point to cam or crank sensor - you could try turning the ignition on, and
unplugging the cam and or crank sensor then plugging it back in. and then trying
to start the engine... often a failing cam or crank sensor will not send a signal to
the ecu, but a bit of voltage kick can send he required signal and the engine will
start. I had a cam sensor that would prevent starting, but unplugging and
replugging it in and the engine would start everytime.
Hope this helps