I had an almost identical thing happen to a work camera I used to look
after - an F828. Same thing - wouldn't turn off!
According to the report that came back from Sony warrranty service
(Australia) - who fixed it very quickly by the way - it was an IC fault
and required replacement of the main board. Whether that is true I
don't know, but it was under warranty and no charge, so I can't see why
they would fib...
As Asaar said, it's generally not easy to discharge an internal
battery. On older devices you could sometimes do it by shorting out
the normal battery terminals with the switch in the ON position (I have
an old GPS that requires this treatment occasionally)... I guess if
you want to take the risk you could try something similar (ie use
something to short the terminals, and also hold the switch down for a
good while...) but you may risk damaging the camera that way. If you
can let it gather dust for a couple months, do so.
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