I would have asked for another room after the ten minutes went by.

Which brand was it? You could possibly go for the 100% satisfaction guaranty.

Going forward, should this ever happen again, you will be getting much better results if

1) You don't stay in the room without working air, ask to be moved to another room

and

2) You try to deal with it at check out instead of later.

After the fact is so much harder in many cases.