There are 6 warning lights in two columns of three. If the warning light to which you refer is the top one in the RH column then it is a warning for transmission oil temperature, not level. If it is the bottom RH light then it is for a plugged transmission filter. The high temperature warning will only light the warning light, the plugged filter warning will light the light and sound the buzzer. I suspect from your description that your warning is most likely the plugged filter warning although how it can sound even before starting the engine is strange, more commonly it will sound once the engine is started, especially with could oil.
From your description of the problem It would appear that you most likely have either a wiring fault, a transmission filter switch fault, or maybe a stuck spool inside the transmission filter head that activates the switch.
Both the power train temperature sender and the switch should be pretty close together, at least one of them ought to be located on the transmission filter itself. How to tell the difference between them is that the temperature sender only has one wire connected to it, the filter switch has two. Try removing the switch from the filter then reconnect it to the machine wiring and turn the key on. Does the alarm still sound..?
A machine Serial Number would be helpful to locate the correct Electrical Schematic for your machine. There are about 10 different models of D4H.