Huh! It's been a long time, but you are very lucky that I was a plumber . . . and that your HVAC guy jogged my memory. It's been years, but I've run into a problem with cheapo gate valves like the ones you have, that could explain your problem.

The type of gate valve you have is called a NRS gate valve (Non-Rising Stem), and they were made in both industrial and cheapo versions. The cheapo versions were common on pools 20 - 30 years ago.

With those valves, what can happen that the internal threads that lift the gate disk can shear off OR the stem itself can break. This often happens after the valve has been closed tightly for months, and then someone attempts to open it. When the stem breaks, the disc is left locked in the CLOSED position.

To verify the problem, you have to unscrew the valve stem from the body. You'd better hire a plumber; without the right tools and the right skill, you can collapse the valve body in the process of unscrewing it. Once the valve stem is removed, you can inspect to see if the threads have sheared or the stem has broken. At that point, you can either replace the valve OR simply remove the disk and reinstall the stem. The valve will then be open and unable to close.