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I'd agree that it could well be the fuel pump not being enabled and the pump relay should be located in the fascia fusebox see the attached image
OK if you have found the pump relay is it turning on?
, replace the relay if in any doubt and do the same for the fuse,
OK please bear in mind I have no idea of your level of experience or what you have tried already
so have your tried a new relay?
have you tested to see if there's spark ?
if you have a scan tool then its also worth plugging that in and seeing if you get an rpm signal coming through
OK, if there's no spark then this is sounding like that the ECM is getting no power or there's no crank signal
and there's no pump relay on this model as all the fuel pump control us done via a pump control module that contains the relays
so there should be a fuse but it will be labelled up as fuel pump control
so as you have had the heater blower off its quite possible that the ECM socket was disturbed and possibly disconnected?
Looks like its tucked under the inlet manifodl
see this video
OK here is a system wiring diagram of the car
https://cardiagn.com/electrical-bmw-f10/
and the actual diagram
https://cardiagn.com/535i-system-wiring-diagrams-bmw-f10/
admittedly its for a 535 not a 528 but the module location and wiring to is extremely similar if you look on p26 you'll see the starting system for the car and there is a DME relay thats fed by the engine electronics fuse centre
there should be a DME / ECM power supply fuse in the underhood fusebox
and as you have no error codes or spark it really feels like the ECM isn't getting power at all
I'm assuming that the dash is lighting up and that its cranking so this means its unlikely to be a security system fault
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