The 104 motor has no "cold start injectors"
If the engine runs smoothly if you disconnect the vac hose to the EGR valve, then one would suspect that vacuum is being applied inappropriately to the EGR valve.
There are 2 switch-over valves on the front of the cylinder head cover, one is EGR, the other is for the AIR pump divert valve. The AIR pump divert valve will activate on engine stat-up IF the engine temp is cold enough. I suspect that either A) the wiring was put on the switch-over valves reversed, or B) the vacuum hoses were put onto the wrong switch-over valves.
Other possiblities is that the engine control module is "whacked" shall we say, or there is a short in the harness somewhere causing the EGR switch-over valve to apply vacuum to the valve. More than likely it is A or B listed above.