I have experienced a similar problem with HDI powered Peugeots. On these the boost control solenoid can go bad and the ECU attempts to make the turbo do something but actually the wastegate stays wide open and doesn't make any boost.
I don't know whether the L series has a boost control solenoid or not.
Another common failure on VWs is with Mass Airflow Sensors. The ECU will not inject more fuel into the the engine than there is air to burn it, and so if the MAF is not working correctly then it reduces power.
Also make sure that your EGR valve isn't stuck open.
These are just guesses though as I have never owned an L series.
Looking at what pscan can do here are the live data parameters that can be monitored
Manifold pressure is there, you can check that you are getting boost.
Pedal position is there, make sure that it goes to 100% when you floor the accelerator.
Air flow is there: maybe compare with another owner of a similar car.