DIAGNOSIS The door isn't fully latched or the child lock is engaged. That three-beep sequence and flashing start button is the machine's way of telling you it can't begin a cycle because it doesn't think the door is secure.
FIX First, open and firmly re-close the door. You should hear a solid, positive click from the latch. If it still beeps, check for the child lock. Press and hold the Start button for about 3-5 seconds until you hear a confirmation beep. The lock icon on the display should turn off. Now try starting a cycle normally.
IF THAT DIDN'T WORK Look for something blocking the door from closing completely. A utensil fallen into the door gasket, the detergent dispenser not fully clicked shut, or the lower rack not rolled in all the way can prevent a proper seal. Clear any obstruction and try again.
HEADS UP If the door seems to latch but the machine still refuses to start, the door latch switch itself might be faulty. That's a repair call, but it's a relatively common and straightforward fix for an appliance tech.