Sounds like you may have a connection problem at the battery I would clean the post real good. It does not take much to drop the power to the other connections when the starter is engaged about 1000 amps or more will rush to the starter and then come down to the cranking amps any resistance at the battery will cause a voltage drop. I know that the battery should be checked also at cranking for the voltage drop it should not drop below 10.5 volts, this may give you a clue to the problem hope it helps.
Hugh
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