What drives the compressor before the turbine provides power?
Turbine engines are spun up to idle speed using a starter.  This is typically in the form of an electric motor for smaller turbine engines and APUs and pneumatic powered starters for large turbine engines.  Once the gas core is spun up to a minimum speed, typically around 12-20% maximum core speed, fuel is introduced and ignited, causing a self sustaining combustion and the engine core spins up to its idle speed, typically about 50% - 60% maximum speed, before the starter cuts out.  Care has to be taken not to introduce fuel to the engine prior to reaching these speeds as the engine can overheat during startup and be seriously damaged (this is about the only disadvantage of aviation gas turbines).