Why Electrical Wall Outlets Don't Work In Only One Bedroom?

Polarity of the connections is a safety issue only, and will have no effect on the functionality of the receptacles. Sounds to me like there is a wire that has simply come loose somewhere in the circuit. Pull the receps, and check all the connection.

I would turn off the breaker to the room and remove the outlets from the wall. Next Check the connections to ensure that there is a solid connection. If the connection is solid, try switching the wires, they may have been installed wrong? They may have the negative wire on the positive screw and vise versa. If that doesn't fix it, the only other option I see is to trace the wires back to the main source of power to ensure they are properly connected to the main line.