sounds like a cracked air intake hose after the afm and before the turbo. pictures of the engine bay to see how everything is set up would help. also ignitor might be toast or the ground in there is corroded?
start checking for fuel flow, ignition, wiring connectors, dist cap, air plumbing, cold start injector (might be running off of the cold start inj then dieing when the timing temp switch turns off) listen/feel the injectors to see if they are clicking/opening.
the problem could be worse like the one i am having with my 7mgte.....