If you are removing VCC from some ICs but they are still connected to other ICs which DO have power, then you could be getting a current drain from your powered ICs to the 'unpowered' ones. Generally inputs to logic ICs have some diode clamping to the VCC of that chip. If you now have an o/p of a powered IC which is 'High', connected to the i/p of an 'unpowered' IC, then there will be some current flow into the i/p of the upowered IC and hence into the VCC of that chip through the clamping diode. This current can sometimes be sufficient to make the 'unpowered' IC operational.
It may be more fruitful if you use low power Cmos devices and if you can 'reduce' the number of signals which are continuously changing state.

Tony