Do I understand correctly that when the power goes out, there is no power to the Dashboard? If so, that is what you should focus on. The dash should power up regardless of the relays and solenoids, or ECU. Ignore the starter circuit for now.
Set the multi-meter to 12 volts.
I would start at the ignition switch, and make sure it is receiving power, and is passing power through when the switch is on. If so, follow that circuit to the main fuse block. If everything is energized, then a bad ground is likely.
Otherwise, if there is power to the switch but not beyond, replace the switch.
The switch should get its power directly from the battery, so if there is no power to the switch, then the connection at the battery is poor, or the feed wire is broken.