Isn't the answer as simple as this?
The compressor is needed to get you off the ground (ramjets are essentially turbojets with no compressor; you can't take off from the ground with a ramjet, without a booster of some sort). A jet engine is essentially a controlled explosion--if you had no compressor, and you were sitting in the ground, all you'd have is a fire in the combustor (the combustor injects fuel into the air stream, which starts on fire, heats up, goes through the turbine and out the back, through the nozzle); you'd get some 'thrust,' as the really hot air went through the turbine and through the back, but not enough to get you off the ground. Now, compress that air 20 times its original pressure, inject some fuel, and light it--voila! explosion! Air rushes out the back of the combustor through the turbine, turning the turbine, (which gives you enough energy to compress the air), the air blows out back through the nozzle.
deepthishan; since the combustion chamber has constant volume, I think you might have meant 'more mass, m' or 'more mass flow, m-dot' ("m" with a small dot on top of it, signifying dm/dt).