If you have a different mic try swapping it out, or try the 19XS mic on a known good radio. Could be something as simple as a broken audio wire in the mic cord.
Does the PA function work? Does it have receive audio? If so, you've just validated the mic wiring, element, and switch, as well as the unit's audio amplifier. Since you didn't mention those functions or a no carrier problem, let's look at what's left between the audio amp and the final.
Check if RV201 has been cranked down. That's the modulation adjustment.
Check if C253 is failed, since that couples the transmit audio to the driver and final. Also a chance that C241 could the culprit.
If you have access to an oscilloscope I highly recommend using it to see if you can figure out where the audio signal disappears.
The 19XS is approaching 40 years old, so it might not be a bad idea to replace the electrolytic caps. This wasn't exactly the top of the line radio in it's day.