DIAGNOSIS The dishwasher is failing its initial door seal check. The three-beep error, usually with the "door" LED lit, means it thinks the door is open or not latched securely, even if it looks closed to you.
FIX First, open and then firmly re-close the door. Listen for a distinct click. If that doesn't work, inspect the door latch area and the metal strike plate on the tub frame for any food debris or a small piece of broken plastic. Clean it out with a damp cloth. A crumb in the wrong spot can stop the latch from fully engaging.
IF THAT DIDN'T WORK The door switch itself might be faulty. You can test this by carefully pressing the switch mechanism (located behind the door latch) with the handle of a screwdriver while the door is open. If it starts, the switch is bad and needs replacing.
HEADS UP Don't just keep slamming the door. If the latch or strike plate is misaligned from an impact, forcing it can break the plastic housing, which is a much more expensive fix than cleaning out a bit of gunk.