I don't think they should be live at both coil terminals. I would unplug both coil primary leads and with the key on check to see which one is live. The other grounds through the CDI unit to one of the safety devices. I don't know if the CDI unit controls the primary current by turning the input voltage on and off to generate a spark or if it turns the ground side on and off to generate spark. Since your CDI unit is a Procom unit from your email, I would try attaching a ground jumper lead directly to the coil primary ground leads and see if that starts your bike up.
Anybody else feel like commenting about how the coils are grounded?
