I don't know if I reported this before, but I discovered that the touch screen issue only exists when the system is up and running. It does not exist in recovery mode, i.e. the touch screen works in recovery but not when the system is fully loaded.
I also found that a mouse, attached...
I'm thinking of reinstalling the OS on my Allwinner A23, since I cannot get the screen to respond; but I'm not sure which, if any, is the right one on this website Allwinner A23 T739 Stock Firmware ROM (Flash File)
As far as I can tell, I have an:
Allwinner A23 (dual core)