Hi all.  The Kimball player could have a bad relay.  When the play
button is pressed, it energizes three relays.  It's not likely that
all three are stuck on.

I would first suspect a short between the wires to the "Start" button.
This would make the play cycle start when the switch is turned on and
also keep the re-roll from taking place at the end of the roll.  As
the Start button is located at the front right of the control area, its
small thin wires can easily get pinched between the metal frame which
is rotated for tuning.

Check around the pivot area for trapped wires.  Tuners do not always
realize how tight some of these wires pull and fail to check for
clearance when closing up after the tuning.

Ferdinand Pointer
The Piano Company
Clearwater, Florida