Time to check the starter. Take the power directly from a battery to the starter via jumper cables, then from the positive connection to the solenoid start terminal to engage the starter. Then you can work back through your existing system.
Have you checked for the starter working with one battery at a time?
If the batteries are fully charged and go blank under load the battery itself can be "broken" inside. The battery will check fine and may even run a few low power draws but when a large amount of power is needed the brake inside will not allow the heavy current to flow.
When engaging and the power drops have you checked voltage at the batteries terminals?
Dave Neptune
