It's important to be very clear on what makes the air dryer purge. The compressor runs, develops pressure. The air compressor is controlled by the air governor. When the air governor senses that a certain amount of air pressure has developed (usually around 120 PSI, it switches so the air compressor stops developing pressure and also sends a signal to the air dryer to tell it to purge. When it purges, all the air stored in the air dryer and the line from the compressor to the air dryer is purged out blowing out any trapped moisture. When the air governor senses that the air pressure has dropped to a set level (usually 95 psi or 25 psi lower than the high pressure cut-out point) the governor switches again, tells the compressor to start to develop pressure again, and tells the air dryer to close it's purge valve.
So if your air dryer did not purge, it's either because it's broken or because the air governor did not tell it to purge successfully. Assuming the signal line between the governor and the air dryer is still intact if the governor did not tell it to purge, it's because the compressor did not develop sufficient air pressure, or because the governor is broken. If the air compressor did not develop sufficient air pressure, its because the air compressor is broken or there is a leak. Knowing that, you can now work backwards and see what the problem is - determine air pressure, determine fault, determine cause, rectify. If only it were that easy in real life...

Brian