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Attached is a rather simple circuit which should work, I think.

When S1 is depressed, it turns on the transistor, and also charges C1.

As soon as the PIC starts up it sets the pin to output and drives it low.
This will latch on the power.

To sense the switch the PIC simply turns the pin momentarily into an input
and reads the state. C1 will hold the power on during this interval.

To turn off the power the PIC simple turns the pin into an input and waits
for C1 to discharge to turn off the power.

Bob Amemrman
RAm Systems

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