DIAGNOSIS Yeah, this one's common. The three beeps and flashing lights are the dishwasher's way of telling you the door isn't fully latched or the door latch switch itself has failed. The machine won't start a cycle if it doesn't think the door is secure.
FIX First, just give the door a firm, positive push to close it. Listen for a solid click. If it still beeps, open the door and check the latch area on the door and the strike plate on the tub frame for any food debris or a small piece of broken plastic. Clean it out with a damp cloth. Then try closing it again.
IF THAT DIDN'T WORK The door latch switch assembly might be faulty. It's a small electrical component in the door that gets depressed when the latch engages. If it's broken, the dishwasher never gets the 'door closed' signal. You'd need to replace the switch, which involves removing the inner door panel.
HEADS UP Before you order any parts, try running a diagnostic test. Hold the 'Heated Dry' and 'Start/Resume' buttons together for 3 seconds. The display will show codes if there are any stored. A code related to the door switch can confirm the issue.