Best bet is to try disconnecting the stereo system from the rest of the electrics.
No doubt you got the fuse by the battery for the amp feed to the boot so just pull it out and start the car, put the beam on and see what happens, If it doesn't do it you know your draining your battery when your amp is on.
If it does do it and you've taken the amp out of the system then you know that its not coping with current it should be able to.