Try pressing the ON several times - mine needs to be pressed hard. If all else has failed I would narrow it down to software issues. Will have to reset the memory somehow. I can’t be of any more than that.
If your calculator only turns ON when plugged to an external device, I would still suspect corrosion in one of the battery terminals. Open it up and inspect it. I don’t think it’s a configuration issue or software.
If neither replacing the 4 AA batteries or replacing the round back-up battery work then I guarantee you have CORROSION on one of the terminals…
Remove all screws on the back (except the one holding the round battery) and look at each of the 4 (FOUR) terminals where the 4 AA batteries make contact with the green board. Clean the contacts and should be fixed after putting it back together.