So there's a lot of chatter lately about resurrecting/creating Jules Verne's old spaceship launching cannon - essentially a big gun on/in the ground that shoots objects into space.
(See this boingboing post for some more info and jump-off links.)
The major issue is one of friction and heat, namely any projectile moving through low atmosphere at enough speed to hit orbit would burn up well before it got there.
So here's a thought.
Let's use the big gun to launch a projectile, but instead of full velocity at exiting the muzzle you make the projectile a SCRAMjet. It'll leave the gun at well above Mach5, trigger the SCRAMjet engine, and roar vertically into orbit, accelerating the whole way. The momentum it's got should coast it through the upper atmosphere where the air's too thin for the SCRAMjet to function, perhaps needing a small booster for the last push to orbit.