I would like a precise calculation of the economics of the rail
launch.  Precisely how much payload and fuel will be saved if we
launch the shuttles from a monorail launch system that launches off
the Rocky Mountains?
Assume the rail will launch the shuttle from about 700 MPH or more. 
What are the cost savings and will we be able to launch multiple ships
within seconds of eachother?  What is the payload increase and what is
the fuel savings?  The technology is the Colorado Monorail Initiative.
 Does this concept bring our space program into the Star Trek Level? 
Does it blow NASA away?

What you've asked really is too inspecific. You need at least to spell
out the payloads you want to boost. Within some spectrum of payload
masses, there *may* arguably be some benefit from such a device. If
the mass is trivially small, it's conceivable that it'll be overkill,
since every payload destined for a stable elliptical orbit must carry
with it its own rocket stage, to adjust the orbit away from its
initial Earth-intersecting path. Too much payload mass, and it becomes
possibly not usable at all for this purpose. The reason being that a
magnetic impellor will only be able to deliver momentum up to some
limit. It'll be accelerating the payload against irreducible resistive
forces and will reach a terminal velocity. And this is not even
mentioning the finite length of the rail.

   Also, speaking of finite rail length, if you want to launch people,
then there's a definite ceiling on the allowable acceleration. If you
launch a steady customer base of average specimens, then 3g is about
as high as it can go. But the rail can only be up to some length; we
can't have it monopolising the countryside for hundreds of miles. The
velocity attainable at 3g over a politically viable length won't be
spectacularly high.

   It's not really a good idea to be launching from the Rocky
Mountains, since failed payloads will be crashing onto towns
downrange. It needs to launch from near the east coast over the ocean.
This certainly limits how tall the exit terminal of the rail can be
made. By the time the payload leaves the rail it needs to be traveling
at some angle between 0 & 90 degrees from the horizontal. If the angle
is too shallow, then the payload will be slicing through a lot of air
on its way to high altitude. In fact, when satellites are launched
from the ground there's a godo reason why they always start out
pointing straight up. It's to get as much atmosphere below it as
quickly as possible. As the air gets thin then it pitches over
gradually as it approaches closer to the target orbital altitude. But
anyway- the rail won't get awefully far above sea level because it has
to hug the east coast. This puts a lot of constraint on how much
velocity it can impart to the payload.

   And finally, it's unlikely that orbital spacecraft will be launched
one after the other rapidly, like airplanes do from a busy airport.
Orbital mechanics is very exacting. Presumably the payload spacecraft
will have some destination. There will only be certain "windows"
during which it is optimal (or often even possible) to launch and
rendesvous with an orbiting target given the very limited propellant
budgets of spacecraft. It's not as if a spaceport can be operated like
an airport, with ships just coming & going pretty much all the time.
It all has to be scheduled rather tightly and efficiently. And even if
a launch window is long enough to conceivably launch several craft in
quick succession, it's not probably a safe thing to do, having all
those spacecraft on converging paths in close proximity.

Escape velocity from the sruface of the earth is 25000 mi/h.
Significantly higher than your proposed 700MPH.

I am assuming that acceleration stops as soon as the end of the
rail/top of the mountian is reached. If you are considering
accelerating the payload with rockets after it leaves the rail then
i'm not sure how those equasions work out.

Certainly I imagine a rocket powered launch after the initial launch catapult.

The specific payloads I am considering are 1. Water, 2. Food, 3. a
lightweight foundry for smelting raw materials and a fabrication
facility.  This should start us off with a space or moon platform from
which to launch into deep space!!??!?!?

As far as the "Star Trek level" goes, the answer is a big NO.  In Star
Trek, they traveled the galaxies searching for new life and new
civilization as they boldly went where no man had gone before.  The
star ship Enterprise took its crew from 1 colonized planet to another
in a matter of hours.

Your scenario still gives absolutely no way to get a spaceship beyond
(or even anywhere near) the speed of light.  The nearest star to us is
over 4 light years away... so even if we happen to reach half the
speed of light (doubtful in my lifetime), it'll take 8 years to reach
even 1 other star.  And we're quit certain that there is no life
there.

Do keep in mind that Star Trek was set in the ... 23rd century I think
it was.  We've got quite a ways to go before that kind of space
travel.  But we are developing technology in other areas that rival
theirs:
laser weapons
communication devices
interactive computers

I'm sure there are trekies around here who could list many more.