DIAGNOSIS The printer is stuck in a failed boot cycle, usually triggered by a corrupted firmware update or a temporary power surge. The flashing light means it's trying and failing to initialize.
FIX Unplug the power cord from the back of the printer AND from the wall outlet. Wait a full 60 seconds—this lets the internal capacitors drain completely. While it's unplugged, press and hold the power button on the printer for about 10 seconds (this discharges any residual static). Plug everything back in firmly and press the power button once. It should go through a normal boot sequence.
IF THAT DIDN'T WORK The issue might be with the power supply itself. Try a different power outlet that you know works, and make sure you're using the original HP power cord that came in the box. A different cord might not deliver the right voltage.
HEADS UP If it still just flashes after this, the main logic board might be fried. HP's warranty process for this usually starts with them having you run the same power cycle steps, so you've already done their first-line troubleshooting.