How can I detect when the air flow in a room stops and report it?
For a very simple sensor you could hang two parallel strips of thin (very flexible) foil in front of the air vent. When air is flowing they'd end up pushed together, giving you (essentially) a switch closure you could read.

You'd still need something to notice and give a yell, like the Arduino + ethernet shield mentioned elsewhere, but this is about as simple a sensor as you could get.