When a molecule hits a surface it imparts a force and were it not for
another molecule directly oposite of it then it would move the
surface. Whether inside or outside makes no difference.
There is only one formula for calculating the movement and it doesn't
ask if the case is inside or outside.
 So why do so many people think it is not possible to upset that
balance causing a closed container to move?

Barring external forces, the center of mass of the object must remain
stationary.  So if the moelcules decide to gang up on one wall, they
achieve this by sending molecules to the other wall, and the forces
cancel out.  So if placed in a vacuum, the object will remain
stationary.  However, if there are molecules on the outside, they can
indeed decide to gang up on the object and act in unison to cause the
object to move.  This effect is commonly referred to as wind.  I hope
this helps.

To tpmii-ga
I think you you know perfectly well that molecules don't think.
So you should. Consider what makes a baseball pitch curv or a golf ball slice.
See why I am asking by studying http://newlifter.tripod.com
When an object hits a surface the force it imparts will be affected by
the angle of approach. The sharper angle the less the pressure. That's
what makes Bernoulli work isn't it.

Well hello again - still working on your perpetual motion machine I see.
In answer to your question, you need to look at what happens after the collision.
To make this simple to visualise, lets pretend there is one particle
in your container (which I personally am imagining as an empty baked
bean can, but hey)
As the particle hits the end wall, it bounces off and there is a
change in the momentum of both the particle and the container. The
container will move away from the collision, and the particle will
bounce back in the opposite direction.
This gives you the movement you are looking for.
BUT
at some point in the future, the particle which is now heading in the
opposite direction hits the wall at the other end of the container.
There is another change in the momentum of both particle and container
- in each case this is in the opposite direction to the previous
collision, and the two changes cancel each other out.
(Note also that the total momentum of particle + container is constant
throughout, it is just how it is divided between the two that
changes.)
So you see, for a single particle over time the container does not
move as the particle tries to move it first one way and then the
other.
Add in all the other particles doing the same thing, and the changes
average out due to the numbers of particles as well as over time.
Result - no movement.
I am afraid the flaw in your plans and previous examples always comes
down to not following the particle through every collision with all
surfaces after the first - this is what cancels out your hoped for
gain in momentum of the container at the first collision.

To lostpost-ga;

"As the particle hits the end wall, it bounces off and there is a
change in the momentum of both the particle and the container. The
container will move away from the collision, and the particle will
bounce back in the opposite direction.
This gives you the movement you are looking for."
That's good as far as it goes BUT when it is hitting the upper surface
it imparts force according to it's angle of approach which is a
sharper angle than when it hits the bottom surface. This is what the
combimation of relative motion and Bernoulli does. Just like what
makes a baseball able to move sideways after it is pitched. Please
don't call it perpetual motion as it is a powered machine.
And remember there are two ways to move an object. Directly apply a
force or remove a counter force that was holding it still. That's what
Bernoulli does (removes a force).     newlifter.com

Your references to the angles are not correct I am afraid. You can
follow my previous argument, but assume an angled impact (and angled
end surfaces if you like)
You can resolve the forces into three perpendicular directions (X, Y
and Z, or fowards and back, up and down, left and right) and look at
each individually. The same model applies - the resultant forces in
each axis will cancel out.

All ideas of this kind fall into the category of perpetual motion
machines as they rely on a physical principle that could be used to
create a perpetual motion machine, as is the case here. This is
usually the simplest test that something has gone wrong in the initial
analysis, but you seem to require proof of your mistake from
elementary principles, which is what I have tried to provide.

To lostpost-ga
"but assume an angled impact (and angled
end surfaces if you like)
You can resolve the forces into three perpendicular directions (X, Y
and Z, or fowards and back, up and down, left and right) and look at
each individually. The same model applies - the resultant forces in
each axis will cancel out."

That would be true if the attempt were to shape a container like you
seem to be  assuming. I thnk you have not looked at the reference  
http://newlifter.com
This project is like a cylinder with rotating fluid and two end covers
also rotating but one clockwise and the other counter clockwise this
puts the fluid between two surfaces moving opposite. One with the
fluid and one against.
That unballances the velocities on the surfaces and the pressure.
Try again.