The D.I. cassette itself gets power through the fuel injection System relay.  The wire color is red/gray at the D.I. connector (remember, this is for a '91; yours may differ).   This same power goes to the Air Mass Meter (connector pin 5), the DI/APC ECU (pin 35) and the charcoal canister vent valve.  All this current flows through one contact of the fuel injection System relay, contact 87B.  The main feed wire from the relay contact branches at a point labeled J76 on the schematic, which I assume is a wire junction point.  (Power to the fuel injectors, the fuel injection ECU pin 9, the idle speed control valve and the coil of the fuel pump relay comes from the other fuel injection System relay contact, contact 87).   Obviously, any contact failure in this relay can shut you down, and it's a very good idea to replace it as a starting troubleshooting measure.

The D.I. gets its ground from a wire that's bolted to the head in the vicinity of the thermostat.

The D.I. cassette receives from the APC/DI ECU a firing Trigger signal for each cylinder.  The wire colors are gray, blue, green and orange.  

The D.I. cassette sends two Combustion signals to the APC/DI ECU.  The ECU sends battery voltage to these connections and the D.I. senses combustion (plug resistance) and sends this info back to the ECU.  I'm not sure if this is a signal pulse or a voltage level shift.

You can check for voltage and ground easily.  Checking to see if the circuit can actually deliver the required current is another matter.  Potential problem areas include the fuel System relay (in the relay panel behind the glove compartment) and the 2" diameter round connector in the aquarium, toward the driver's side.  If you hear the plug-cleaning buzz after the ignition is shut off after cranking, then it would seem very reasonable to assume that the D.I. is firing the plugs, as the noise is the plugs actually firing.  NOTE: You must crank the engine first; when the key is turned to OFF, you should hear the buzz for 5 seconds.  If you do not hear the plug cleaning noise, you can check for trigger signals from the APC/DI ECU, assuming that you can get your hands on an oscilloscope (I could not see any measurable AC or DC voltage with a meter).  The Trigger signal is a negative-going  pulse (1/2 millisecond or so, from battery voltage to ground).  The signal should be present on each of the trigger lines while cranking.  Picture.  When you stop cranking and return the key to the OFF position, the trigger voltage should go to ground momentarily, then to battery voltage, then the pulses will fire for 5 seconds at a rate equivalent to 6000 RPM (this is the plug cleaning cycle).  If you see the pulses but don't hear the plug cleaning buzz, then either the D.I. cassette is bad or you're not getting enough current to the D.I., in which case you can check the fuel System relay and the round connector.

The Trigger pulses are generated by the APC/DI ECU, based on signals from the crankshaft sensor.  If the tach needle bounces when you crank the engine, the crankshaft sensor is working.  NOTE: I'm not sure if the tach needle bounces on earlier models or not - on my '94, it rises ever so slightly off the peg under continuous cranking, only about a sixteenth of an inch, and it is very steady.  If the tach needle doesn't bounce or move off the peg at all when cranking and you can't see any Trigger pulses, then the crank sensor is bad or the wiring is messed up (it's a shielded cable, so it can be damaged).  If the cable shielding gets messed up, the circuit can become susceptible to electrical noise, which would cause erratic operation.