Center vent not blowing air hot or cold?

Sounds like the mode control linkage has an issue. Honda uses a mode controller that moves the air doors to control airflow using a few linkage arms that move depending on where you want the air to go. If you can select defrost or floor and those work but not the dash then it is the linkage, if you select them and it doesn't change from defrost to floor then it is most likely the actuator. Both items are not that hard to access. To get to them you need to remove the glove box, for that you release the two taps in the lid then remove the two bolts from underneath the hinge and set the box out of the way. The linkage and actuator will be visible inside the door opening to the left side. To test it simply turn the key on and select the various airflows, so defrost, dash, floor. Watch the movement of the arms behind the actuator (circled in orange). As the airflow changes, those should move. I've seen the screw that secures the front lever come out and the arm doesn't pivot the way it should.
The other item is the pin that moves the linkage breaking off. If you are handy with a drill that can be repaired by drilling through the arm and cutting a nail down and epoxying it in place as a replacement, or just visit a salvage yard and get a good one. If the actuator itself is the issue, unplug the wire connection and then remove the screws, test the linkage and reverse the process to install the new one.

There are two actuators there, one is the passenger temp actuator the other is the mode unit, The upper one is the mode control, the lower one that is moving should be temperature control. So, if you can adjust to hot cold and see that move but not the mode then it's the actuator or the cm pin on the end of the arm on it. Easy enough to check it, just remove the screws and pull it out. The pin is a common failure, but they don't sell just that part. If you can get it try the Standard Motor Products ADR4267 and try to avoid the Dorman one, it's not a hard part to replace but you don't want it to be a yearly thing. Thanks for the video, it makes it a lot easier.