I bought an untested 2nd-hand HP probook 645 g1. When I plug it in, the power button just flashes. It does not look like an error code. It flashes every second or so. No long flashes and does not pause. It’s uniformly separated blinks that never stop.
It does this with or without memory installed. There is no hard drive but I don’t imagine that would stop it at least booting to the BIOS. I tried removing the wi-fi card and CD drive to ensure there is no problem to detect on those components. I also tried unplugging, removing the battery, and also detaching the cr2032 CMOS battery for some time. No matter what, the power button just blinks when it gets power. The power button is non-responsive.
What might the issue be?
One friend’s theory is that the machine is extremely fussy about the brand of PSU. I am using a Dell PSU to power the HP. It is 19.5v, as specified. So in terms of physics it should work. My friend’s theory is that genuine OEM HP PSUs give 19.51v (for example) and HP is somehow detecting that it’s not an HP PSU. Does that sound plausible?

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.