Welcome to genvibe.
There's things that cause the heat to not work, and there's things that cause the AC to not work, but identifying one common cause for both is a challenge.
The only thing I can think of would be the blend door control. The temperature control in the dash moves a mechanical cable that moves a flapper in the air distribution system. In these cars, there is heated engine coolant always running through a heater core in the center of the dash, and the door controls how much air gets passed through that heater core. When you set it to hot, all the air goes through it, when you set it to cold, none is supposed to go through it.
There was a common problem in the first years where that cable was not aligned properly, causing some air to pass through the heater core even when set to max cold, causing the AC to not run as cold as it could. A thread on that is at
viewtopic.php?t=1004 unfortunately the pics form that thread have disappeared.
Seems a long shot, but perhaps that control cable has come off somewhere, and the door is partially open. I'd think that you'd still get some heat coming out if that were the case though.
Now maybe the AC quit and the blend door is stuck in the cold position.
If its' independent issues, then
A likely cause for no heat is an air pocket in the heater core, this can happen if the coolant is changed and then the system isn't properly burped.
AC failing in Vibes tends to be either a leak and the refrigerant level is low, or the AC compressor clutch has failed.