The Space Elevator will never happen : LIGHTNING : both the 400,000V potential difference(average flow 1800A worldwide)and the Debye effect(reactive ions in orbit). If there is even a HINT that these science fair teeny boppers will short out that spherical capacitor and drastically change our biosphere(no 50V/meter electropotential gradient)with their elevator cable, the cuffs will be on them pronto........Yes, one pound to LEO runs about $20,000 on the shuttle. The actual energy value(mv^2/2 + mgh)of one pound in LEO is 4 KWH, or about 40 cents @ 10 cents/KWH. Arthur Clarke began to expound on that during an Apollo launch when Jules Bergman(remember him?)cut him off like a meat cleaver, NASA doesn't want you know how BIG their markup is : $20,000 for 40 cents worth of work......Thus it was that in the 1980's, during the salad days for SDI, a small slice of the aerospace community proposed EMSL : ElectroMagnetic Space Launch : shooting artillery projectiles into LEO at some 10% efficiency($4/#). The best idea, in my opinion, was the quenched superconducting ring-cannon(about 300 ft long to achieve 5 mps injection velocity). The studies were quite extensive, it looked very feasible, but nasa squelched it : it was too good of an idea which meant the ROCKET SCIENTISTS might have been out of a job. It's called VESTED INTERESTS, and no VESTED INTEREST ever funds its competitor...
Nope, not a space elevator (although he may discuss that on his long, long page). Space elevators won't work, and it hasn't to do with material strength, it just can't be deployed and/or stay put. Not too sure about the lightning problem "timer" mentioned, that might be fun to watch (from a safe distance). ;')