Why are my flash and trigger not talking to each other?

Make sure the trigger is fully seated in the hot shoe because this is the most common cause of flash equipment suddenly not working.

A second common cause of flash not firing is setting the camera shutter speed above the camera’s maximum sync speed. It is not uncommon for cameras to disable flash firing electronics when the shutter speed is too high.

That the flash works on the camera hotshoe means you've eliminated the camera hotshoe and the flash foot as potential issues. And that the Test button isn't firing the flash eliminates camera flash modes as an issue.

Assuming your flash triggers are the rebranded Godox CT-16 manual triggers that Neewer tends to sell with their flashes :) Here are some things you can check in general when it comes to triggering misfires:

• Are the batteries in everything in good health and fully charged? (Low charge can be a culprit, and a battery in bad health may look like it's fully charged when it's actually not capable of holding full charge).
• Is the transmitter seated fully forward and locked down in the camera hotshoe? If the sync pin on the transmitter isn't making contact with the sync contact on the hotshoe, the signal won't be communicated.
• Similarly, is the flash seated all the way forward and securely locked down into the hotshoe of the receiver?
• Are the transmitter and receiver units set to use the same channel? (The dip switches on the receiver are exposed, so could be knocked off.
• Is there nearby radio interference? Have you tried switching channels or moving to a different location farther away from, say, wi-fi routers or other 2.4 GHz radio gear?
• Is the flash set as if it were to be used on-camera? (I.e., out of any wireless slave modes?). Using a built-in optical sensor or radio receiver as the triggering method may disable the flash's foot.