Our coffee maker used to do that (turn on randomly). Since your tv (or the amp anyway) actually was on, it wasn't just in your mind, or hearing things you know? Which must have been some kind of reassurance, yes? As for waking up and briefly hearing it again, it was probably just your mind doing a checking thing. After all, we certainly don't expect our appliances to turn themselves on, and it probably disconcerted your mind just enough to want reassurance. Especially as you were having trouble sleeping already, your mind was already in a more active/alert state and poised for thought or re-thinking. I hear small things that aren't real (like a phone ring --not even in my tone, lol), and don't consider them hallucinations, as they're not persistant or troubling. I think they happen to "normals" from time to time too. But that's just my take. If it particularly troubles you, mention it to your doctor.

Sorry you had the sleep disturbances though! suga!
Think it's night time there now? Wishing you pleasant tonight...