You aren't the first person this has happened to. The heater core box has a few doors that move around to direct where the heat goes. A little motor, called the "mode door motor" moves them around. Each is connected by various linkages and plastic gears. The top reasons yours could not be working are:
1) the mode door motor itself went bad (I suppose there's a relay for this, that might have went bad too)
2) one of the linkages is disconnected or broken, preventing the doors from moving
You can try taking some of the lower dash trim off (and possibly your radio + bezel) etc. and having a look, basically just to see if anything stands out. The heater box itself is dead center under/behind the dash so its hard to get a look at it. Look on Google images to see what it looks like.
Here's a link to the FSM that talks about the heater box and its controls, not sure exactly what page you will need, but its close:
FSM HA - 107