ADE = Axis Drive Enable
ZAP is a emergency stop condition generated by the FMDC because it saw a problem. The only way to see what caused it is to use the FIST event monitor. This is a diagnostic tool built into the FMDC board using a PC using RS232 communicating with K3 on the FMDC board. It is the maintenance manual.
With a high degree of certainty you have a BOSS 8 which has a two line LCD display.
What you do not say is does the Z move down and back up, is it followed by the y moving away from column and then back to column, and then does the X try and home and is it then that it goes to ZAP.
Lets say it is the X. Does it move off the home switch and back on? If it does not move off the home switch by itself (if it is on the switch) then it does not see the switch. Might be a bad switch or broken wire. Maybe the switch is full of coolant.
If it moves off by itself and back onto the switch but goes to limits, it may not be adjusted correctly or the marker pulse may be missing from the encoder (bad encoder, bad cable, or bad board).