Amira Liakum (asking a non jew to do a melacha)is only prohibited in two types of cases.
1) Where you get a positive benefits and he did it for you. By positive I mean If it's causing a new source of pleasure (he turned on the TV) that would be assur. But taking a way a source of discomfort is not considered a benefit here.
2)You asked him to do the melacha even if you don't benefot at all.
(source: 39 melachos book. I don't remember it's source.)
So since you asked him at first glance this is assur. However if one holds electricity is assur because of Molid (Like rabbi henkin and therefore is Drabbunun), when you ask a non jew (which is assur drabbunun) to do a Drabbunun it is whats called a shvus dshvus and is permitted for a sick person, a mitzvah, or a "great need" (Source 39 melachos book and Rambam. And yes "great need" is very vague). So in this case the person should especially ask their rabbi whether this is considered a "great need" or even a "sick person". If one holds electricity is assur Draaysa then no you can't ask. You could send a child over to ask I think or hint to him.
In regards to listening to music, you didn't ask him to turn it on and he did it for himself so it's not assur from Amira Lakum. Seemingly this would be no different than if you left music on from before shabbos and bring up questions of Uvdin dchol.