When you say dies do you mean goes to limp mode (ie limited to 3k revs) or just 'gagging'? How quickly does the issue clear? You say there;s nolight on the dash. Are you sure the engine management light - usually a pictogram of an engine block with an injection harness and known colloquially as the 'K' light - is illuminating on start. It should do a 'power on self test' in same way as ABS, airbage etc lights.

If you're not seeing it all then either bulb has gone or it's been disconnected.

I'd start by carefully checking all the induction pipework looking for perished or split hoses. On my similarly powered Xantia one of these was subject to both thermal stress and movement when engine flexed on its mountings. Result was K-light on and limp mode until next restart. if you floored it too hard.

There are also potential issues with electrovalves in the turbo circuit which can cause similar symptoms to above or just a milder hesitation or 'gag'. Again though these will normally bring on k-light and generate a fault code.

If inspection of piping finds nothing I'd suggest a visit to a dealer or Peugeot/Cit specialist who can download any fault codes the ECU is retaining.