I got five bleeps when my timing belt snapped and the engine was being cranked. So nothing wrong with my crank sensor, so it must have been something else. On the TDi injector No3 there is a needle lift sensor. When the injector operates (by fuel pressure) the sensor knows the injector has worked and passes this to the ECU. Now on my other car (a TUD5 diesel engined Rover) I had a hole in the fuel pipe, tiny tiny thing. But sometimes the air drawn in through the hole was enough to cause the car starting problems as the air is more compressible than fuel it takes time to get through the injectors. If this was happening the injector sensor would be showing a fault. (It is the brown plug in the photo above btw) So it is a long shot, perhaps you are getting air drawn into the fuel line. Open the bonnet, remove the beautification cover, start your engine and look at the clear plastic pipe going into the fuel pump, there should be no air bubbles flowing through the pipe. Easy to check, probably not the problem, but you never know.