Broken vacuum line next to yellow line for heater door

I had a garage do some engine work in the summer and have not needed to use the heater until now. Switching from defrost to any other setting besides OFF makes no difference. The door position does not change. During a visual inspection, I noticed the yellow vacuum line (very tiny plastic line) was intact but there apparently used to be a black line next to it (under the hood near the passenger side upper firewall). I cannot find where that line comes from. And I am assuming it is part of the problem. Where does it go? I looked all over the firewall but don't see the other end of it hanging anywhere. And could it be the problem? I am an engineer, not a car expert. Please let me know because otherwise it is going to be a cold winter. I cannot afford an expensive repair, which is why I still have a 14 year old car that needs to last until the Spring.