By the way, I was always checking SMART every week, like I do with all of my drives, it was always in pristine condition.

See if it draws anything; and check the efuse. You can also inspect w/a thermal camera to isolate hot spots.

It's the e-fuse, bridge vcc in and out for recovery or replace with another IC .

Start with the IC circled in red on your final picture, remove it (keep it safe) and retest the VCC rail for shorts. It only hits a couple of caps and then disappears into the pmic, I expect the heat you see elsewhere is just residual.

but I am kind of lost about "vcc rail" is it 5v SATA power?

You can see Vin and Vout in the manual. Check Vin and and Vout with your meter in resistance mode and one probe on ground - if either are 0 that's bad. Once you have done that checked those check the resistance to ground of each of the rails from the pmic, francs probably already posted his test points but each of the inductors will do anything 0 ohm is not good.

If you're beeping you're probably in diode mode, if this is a client device you really need a little more experience before offering to work on them.

You should be checking the PCB not the IC iteself. All 3 Vin (1,2,3) pads are joined so you should have continuity between the 3 of them, if the last one of them beeps when checked against ground all of them should you likely had the probe misaligned on pad 3. You should not have continuity between any Vin and ground (pad5 / screwhole). Likewise you should not have continuity between Vout and ground (10,9,8) and ground (pad 5 / screwhole).

Check and confirm.

If you're showing a short on the IC itself it sounds very much like you have found the problem. I am concerned you are getting a direct short to ground on Vin though, there's not exactly a lot between the sata power connector and the fuse to go short, just 1 cap.

Check for a short between ground and the 5v rail at the sata connector itself to be sure. After that there are only 2 resistors and a cap on the back of the pcb before the fuse.

They're not fuses, just resistors. Your measurements aren't making much sense. If you have no short to ground on either side of them you should not have a short on any Vin pad. You have removed the efuse from the pcb haven't you? Check the pads are clear and not bridged and double check pads 1,2,3 for continuity to ground.

The cap : Find the plastic pin in your red circle, move up to the 4 empty horizontal pads , move left to the tiny vertical cap. Should be ground on 1 side only - the bottom pad is on the same plane as the bottom pads of the 2 resistors so I can't see how it would be anything other.