If the coils and electronics for the accelerator cost $1000 per meter, total for the accelerator is under half a billion. The wildcard is the cost of the diamond (and the ability to fabricate it into structural beams). Diamond is a bit expensive today! If an Apollo-style (and -cost) project could do for diamond what the original one did for electronics, we could build the tower in the next decade or so.
Depending on the level of nanotechnology, diamond might cost $100/kg
like graphite for golf clubs and tennis racquets. Diamond costs much
more than that today but there is no mass production -- no one is using
it as a structural material. A mature nanotechnology with self-replicating
assemblers would push cost toward the cost of inputs; carbon in the form
of coal can be had in quantity for as little as $0.02/kg.
The other major part of the cost of a launch is amortization of the cost of the tower. If we can launch once an hour (and at an interest rate of 8%) we must charge $0.91 per kg per billion dollars of tower cost. If the traffic is there the rate might be increased (and the cost reduced) by a factor of 10 but not 100. (NB: as payload size is increased, power costs go up per launch but not per kg; amortization costs go down per kg; and more kinds of things can be launched in one piece. The main limit is the accelerator. Chances are you could build one to handle 10 tonnes, but that's a guess.)
Also, your payload needs to be a spacecraft capable of some 330 m/s
delta-V to circularize its orbit. Orbits decay rapidly at 100 km, which
is why the tower is not in much danger from space debris. The best strategy
is to inject into an orbit whose energy is the same as the desired circular
one, and do a correction at the point the orbits cross which only changes
direction. This is not a Hohmann transfer, which optimizes total delta-V.
With the launch tower, delta-V at correction is considerably more expensive
than at launch, so we minimize it preferentially. Even so, given typical
chemical Isp's, propellant for correction is some 10 to 15% of gross vehicle
weight. For freight that can be a cheap one-shot strap-on solid rocket.
For passengers the vehicle needs to be re-entry capable in case of accidents,
and gets expensive.
Molecular manufacturing, even of a fairly unsophisticated form, could make it economical. Suppose means were found to manufacture diamond and graphite fiber of 5 GPa compressive and tensile strength respectively, in quantity, at $10/kg. If the structure needed half a million tonnes of material it comes to $5 billion. Then the whole business might cost $10 billion. (For comparison, the space station is costing $20 billion and Apollo cost $24 billion in 1960's dollars.) This gives us a total cost of about $10/kg to orbit. This is nearly cheap enough to make ground-launched powersats feasible, but vacations in orbit still cost $25,000.
With a mature nanotechnology, the cost of diamond comes down and the
strength goes up. Likewise the high-tech stuff in the track, and power
generation, and so forth. (An example: recent progress in micron-scale
vacuum tubes suggests that nanoengineering could make high-powered switching
apparatus that was more efficient and cheaper than silicon.) Cost reduction
on the order of 100 seems quite feasible. At 10 cents/kg to orbit, the
Solar System is our oyster.