I can think of three possibe issues and how to isolat them
Number one with a staple gun is a wiring issue.. Some idiot stapled the wire THROUGH the wire (Why it's #1 with a staple gun) and the staple finally cut through two of the wires. Yes, those two, the two the T-Stat connects together to signal "Hey, it's hot in here, cool me off"
#2, Defective stat
#3 Defective control board in the A/C.
Alas, that is a bit like saying "The problem is between the soul of your shoes and your hat"
But here is how to narrow it down
Carefully label and disconnect and tape off all wires at the T-Stat
Problem goes away, It's the stat.
Problem remains,, Re-connect T-Stat (See note below)
Disconnect at the Air Conditioner end .. Again do not forget to label carefully
Problem goes away, Wire, Problem remains, Control board.
NOTE: Some T-Stats are "Socketed" you can very easily remove the T-Stat from teh backing place, inspect for visible shorts where the wires connect and fix if found,, If this is the case, you do not need to label and disconnect. Just unplug.
Home is where I park it!