Car shutting down after start after idling for 3 seconds

[mitch.storrie]

The Vehicle in question is a 2010 Polo Diesel TDI 6R 4 cylinder 1.6L 60kw engine.
I have been having ongoing problems with this vehicle since I purchased it second hand back in 2015. The first problem identified was one of the injectors was quite sluggish and misfiring eventually coming to a complete halt. This was replaced and after this ran fine.
The engine seemed to always run sluggish after and sometimes would lack acceleration coming on and off at times. This is not to do with the natural fact that it is a diesel. The problem gradually got worse over time and now the car will not start.
After plugging in OBD2 device and Bluetooth connecting to my phone the following codes have been displayed. With the following meanings:
Fault Code P2454 (Diesel Particulate Filter Differential Pressure Sensor Circuit Low)
Fault Code P0403 (Exhaust gas Recirculation Control Circuit)
I have taken the car into a Volkswagen dealership earlier in the year and they recommended that the following parts be replaced from their diagnostics.

Parts Numbe Part description Further description
059906051C SENSOR Audi DPF Pressure Sensor
6R0820045Q CONTROLS Heater Control Panel,

Further research into the parts found that the sensor was being quoted for replacement, after speaking with the floor manager at Volkswagen he indicated that it could be possible this sensor could be causing the lagging issues with the engine. The car has been placed on the pit and had particulate run offs frequently. Would it be likely that a failed sensor such as this could be the reason the car starts up. Runs on idol for nor more than a few seconds and then shuts off?