according to the wiring map i have in front of me the power transistor, coil and dizzy (including CAS) take their power straight from the ignition barrel.
the way the diagram is drawn if you have one power supply problem here it could easily affect the lot. think your best bet is do as jon suggested first and make a known good supply of fresh volts for it all
there are 2 wires from the coil/transistor to the ecu
there is 1 wire from the ecu to the power transistor (to control the coil)
and the other is the rpm signal for the ecu and tachometer
the multi connection plug attached that leads to/from the dizzy has 4 wires... 3 of these are the cas, i assume the other is the +ve feed.
There is a tab on the upper side of the dizzy with a push on spade terminal, tbh i'm not sure what that part is

, but ive run it without it connected and nothing monumental happened

and to top it off its not on this wiring diagram

i wouldnt expect this to be the positive feed seeing as the connection isn't secure enough...
theres a guide on doing ecu self diagnosis in the how to section