I'm going back to "hardware issue" with the
keyboard.
You might try plugging a standard 101 keyboard
into the PS2 connector on the back of the laptop
(while the power is off). See how it behaves in real
DOS.
I've hesitated to recommend trrying this before,
because this is what I was doing when I blew out
my first laptop keyboard -- which behaved exactly
as yours is behaving now. Nobody was ever able
to explain why using a full-sized keyboard (which is
what the PS2 port is for) should cause a problem with
the built-in keyboard. But it seemed to, and I had to
replace that built-in keyboard.
Jerry