Welcome to NICO! First step is going to be check the ecu for codes.
http://xenonzcar.com/z31/ECUcodes.html
The bad news is just because something should present a code does not mean it will. So the codes are not an absolute but a good starting point.
Next check the fuses and fusible links (the little black boxed next to the battery).
The injectors are fired based on a signal form the distributor, the distributor sends out 2 signals, one to fire the spark and one to fire the injectors, the distributor would be my primary suspect. It's pretty easy to check if you have a logic probe or similar.
There is also an injector relay but relays seldom fail, but are often suspected.
Lastly it could be the transistor inside the ecu that fires the injectors, which means a new ecu.
hope this helps, let us know what you find.
also I'm moving this to the correct section.