Could a plane with an electric turbine engine generate enough lift to provide a electric areodynamic lift and runway to space?
Assuming maximum altitude for the highest blimp is 74,000 feet, and the rail to be angled at 15 degrees, it gives us a rail length of 285,000 feet. The HiSentinel stratospheric airship flew that high, and was able to carry only 36 kg.

The steel rail/rope would weigh roughly 5.5 million kg. Based on steel density and a good sized rope, to withstand the elements. So we'll need 154,000 blimps to carry the rail. That's 1 blimp every 2 meters. Blimps are huge.

While the idea is highly imaginative (good thing), engineering tends to solve problems, not create ones. Would the blimps (if they fit in the sky) power down between launches? Or stay aloft?

You might want to check out the Stargazer:




  [A] Lockheed L-1011 TriStar that was modified to be used as a mother ship launch pad for Pegasus rockets. As of June 2012, 35 rockets have been launched from it.




RE: How much lift could an electric engine powered plane provide if the power source was provided externally?

What you are asking is like having a plane not carry fuel and instead have a long fuel hose attached to a fuel pump on the ground. Ignoring all the problems associated with that, one will help you understand the problem: pumping the fuel.

Pumping electricity over such a long wire / rail will require high voltage / low current (just like power lines). Which means the E-Fan-like plane and all the blimps will need to carry their own super heavy transformers (as I wrote above, one high-altitude blimp lifts 36 kg, which we've already used for lifting the rail).