If your pump unit is not airlocked there may be debris in the actual pump valves. Airlocked is when there is air in the water line. To undo this, you take out the furthest nozzle and run the pump. The water should shoot out of the nozzle port like 3 or 4 feet. Once it comes out in a steady stream the air is purged, replace the nozzle and it should work. If the water doesn't shoot out but dribbles you can try doing this. It is more intricate but is usually the reason why it's not building pressure. The photo shows our PRO 75 pump but  all HydroMist pumps have the same valves as well as the Cool Caddie.

Here are where the check valves are located on these pumps

They are underneath each of the brass caps on the pump head.

Inside, you'll see that the check valve is inside of the pump head.

I have found that when I take these out, they might come out in several pieces.

I usually use a pair of needle nose pliers.

1) Plastic Top Support

2) Spring

3) Plastic valve body (the smallest plastic part)

4) Stainless valve seat

5) O-ring seal

Usually when these valves stick or have debris in them, they pump will not build pressure.

Each time the piston strokes back and forth, it pushes water through the pump head and opens and closes these valves to build pressure in the system.

Please check to see that they are clean and moving freely up and down before re-installing them. If they need replacing, we sell the kits on Hydromistusa.com

https://hydromistusa.com/promist3-35-pump-check-valve-kit-for-misting-pumps-6-valves-per-pump/