The PSU would be my first guess. Most laptop PSUs have 3 connections rather than the standard 2 for DC barrel jacks. The third pin is to communicate wattage or compatibility.

Here’s HP’s error codes list which shows that blinking power indicates PSU: https://support.hp.com/us-en/document/ish_1997719-1528356-16

Worst case is that the motherboard power circuits are toast.