I'm not sure if the 2001 model has the same injection system as the Mk2 Ulysse, but it is probably similar. I would start by checking the pressure of the fuel coming from the fuel filter to the HP pump. This can be done by using a dial air pressure gauge clamped to a length of plastic hose and then attaching it to the output connector on the fuel filter. The pressure when you switch on the ignition should rise to around 2Bar.
If the low pressure side of the fuel system is OK, you will need to connect a Lexia or Peugeot Planet 2000 diagnostic system to the car's diagnostic socket. Selecting the engine ECU "Parameters 1" option allows you to see the value of the fuel pressure in the common rail. This needs to reach around 170 Bar before the ECU will open the injectors and allow the engine to start. Lexia/PP200 diagnostic interface leads/software are available on Ebay for under £100. Load the software on a laptop, connect the interface lead to the laptop's USB port and you have a diagnostic system for your Ulysse.
One more thought, there is a small valve in the inlet pipe of the HP pump which is supposed to open at 0.8 bar. If this sticks, it could prevent fuel reaching the HP pump cylinders. If you remove the fuel inlet pipe from the HP pump, using a suitable diameter drill in the inlet pipe orifice, it is possible to feel the valve springing back after you press it in. For a vehicle that has been standing unused for 3 years, it is possible that this valve has become stuck shut. Manipulating it with a drill, or similar tool, should free it.