I have front end or transmission issues. Im at a lose

I was driving and
had to slow
down and when I
pushed down on
the throttle to
speed up it was
like it was put in
nuetral. No
forward gears or
reverse. No
check engine
light. No noises
or anything like
that was going
on. Changed tr
sensor. Still
nothing. With the
front end on jack
stands I put the
car in nuetral. If
its a limited slip
should you spin
one tire and the
other will turn in
the opposite
direction right.
You can only
spin one at a
time. With the
tranny in park
the passenger
side locks up like
it should. The
drivers side
doesnt lock up.
You can turn it
but its not really
easy. You dont
hear anything
grinding or
something like
that when you
spin the tire with
it in park. Any
ideas?