[quote=“jetlounge”"]
Either you have juice or not, no?
[/quote]
No.
OK from now on for every technical post looking for help without even stating the make/model of the car I am going to kill a kitten. 
So you own a supercharged Toyota. Is it a factory TRD supercharger? Is your car under warranty?
If the amp is drawing a ton of power, it will drop the voltage in your system and the little electronic bits will see a high current to compensate. This will heat shit up. If you have delicate relays in your computer they could theoretically be damaged by this low voltage/high current situation.
300w isn’t much, so it’s not likely, but apparently something killed your system. :gotme:
It sounds like the dealership doesn’t know what the problem is, but blamed it on you so that when it comes back they don’t have to warranty it. I’d have the dealership remove the sub/amp now and get a receipt that they did it so that when the problem comes back they can’t pin it on you.