Welcome back:
Interestingly, that code is relevant for both engine and transmission. As far as the transmission, if the battery voltage of the Transmission Control Relay Output Sense circuit(s) to the PCM is less than 10.0 volts for the period of 15 seconds a P0562 is set. Generally speaking, it indicates a gradually falling battery voltage or a resistive connection(s) to the PCM. Here is a list of thing that could be at fault. These are right from the manual.
POSSIBLE CAUSES
- RELATED CHARGING SYSTEM DTC'S
- GROUND CIRCUIT OPEN OR HIGH RESISTANCE
- FUSED B+ CIRCUIT TO RELAY HIGH RESISTANCE
- FUSED B+ CIRCUIT TO PCM HIGH RESISTANCE
- TRANSMISSION CONTROL RELAY OUTPUT TO TCM OPEN OR HIGH RESISTANCE
- TRANSMISSION CONTROL RELAY
- POWERTRAIN CONTROL MODULE
- INTERMITTENT WIRING AND CONNECTORS
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As far as it being an engine code, it ties directly in with the idea that the battery voltage is low. I realize you replaced the battery, but many other things can be the cause. There could be excessive resistance between the alternator and the battery allowing voltage to drop as well as a ground or connection issue.
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Do me a favor. We will start at the simple end of things. Lets confirm that the battery is being properly recharged when the engine is running. Even a new battery can fail if the alt isn't doing its job.
It's really simple to test. Follow this link. All you really need is a volt meter. Additionally, reconfirm the battery cables are tight and clean and the ground between the battery negative and both the body and engine block are clean and tight.
https://www.2carpros.com/articles/how-to-check-a-car-alternator
https://www.2carpros.com/articles/how-to-use-a-voltmeter
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Do this and let me know the results.
Take care,
Joe
Sunday, October 13th, 2019 AT 7:50 PM