Sounds like you are using a power antenna lead (which only has power when the tuner is being used) on the HU as a remote lead instead of the remote lead (which has power whenever the HU is on). What model is your Kenwood?
Typically, the remote turn-on lead is blue/white and the antenna lead is solid blue with Kenwood units(Assuming yours has both)
As for the distorted sounding music, is that with all sources (radio, CD, USB, Bluetooth, etc)or only certain sources?