Has a jet "engine" ever been made that only uses the thrust from the bypass air and doesn't have a combustion chamber?
Well what you are describing is a ducted fan.  They are common on RC aircraft with the fan driven by either a gasoline engine or electric motor.

On large scale applications like an airliner, you have to find a source of power for the fan that is 1) compact 2) light weight 3) delivers a very high specific power and 4) draws energy from a reservoir with a high energy density, all while remaining 5) extremely reliable and 6) safe.  For these kinds of applications, you really can’t currently do better for this than use a kerosene fueled gas turbine engine to drive the fan.  And that's all a high bypass turbofan really is - just a gas turbine powered ducted fan.