Chosen Solution

Kindle has been unable to charge and has been dead for 4 years. Opened it up and reattached the charging port. Now batteries at 4 volts. tested power switch which still clicks and test 0 ohms when pressed. held power button down for several different periods of time. Nothing. Charged for hours. Still Nothing.

@glblac5 just because your battery sows some voltage does not mean that it provides the amperage needed to power your Kindle. I suggest that you replace the battery with a new one and then re-evaluate. If nothing else it will provide you with a known-good starting point should further troubleshooting be necessary.