What is a "core lock" on an jet-engine?
There is a good writeup here that explains the engine issues as well as the rest of the incident you mentioned.

Core lock happens when parts inside the engine cool off at different rates, causing interference between them. In the case of the CF34 engines on these Bombardier jets:


  GE isolated the problem to contact between components of the high-pressure-turbine interstage seal - a static, pressurized honeycomb component - and the rotating seal teeth on the outer torque coupling.


Working on getting a good illustration of what they are talking about.

This does not mean that the engine is "not functional." There is just much more resistance on the rotating components, but once the temperatures have time to equalize, the components will break free.


  According to the NTSB, FDR data indicate that the engine cores were beginning to break free just before the impact.


During core lock, the resistance makes starting the engine more difficult. A windmill start does not provide very much turning force on the engine components, so the resistance from core lock makes that method of starting difficult. GE has done engine testing, and when the windmill restart fails, they are able to use bleed air from the other engine to restart the engine, which provides more turning force.