I think the best way to answer why not is to consider PS4 fat HDMI ports compared to PS4 Slim/Pro HDMI ports: They're upside down/backwards! Luckily, a Slim HDMI port costs less than $10, so the question is moot. Just use the right part. Oh and on Slims, white light no display is almost never the port anyways.

Only if the cord itself is damaged.

Please leave emotion at the door. Complete, factual statements are more helpful. If it's blue light then off, it is not a blue light of death. It's normal for the blue light to come on when the console is powered on. If it flashed blue forever, without ever going white, THEN you have a blue light of death. Since it's not a BLOD, trying clamps (washers?) was not only not possible to fix your problem, but could actively have done some damage. It also can be helpful to be specific as to how long the blue light stays on. Simply put, you may have a bad power supply. If it's not the power supply, then it's going to be something on the motherboard associated with power management. Unless you're experienced with this, trying a new power supply is all you can do. Make sure you order one with the same part number as the one you have. Or the alternate part numbers found here: PS4 Dev wiki

There is a small board with the intake motor on it. On 1200s and Slims, it's called KLD-00X. I forget what it's called on a Pro. but they're all interchangeable. Anyways, there's a few switch on that board. If it's taking the disc all the way in, but not spinning, I'd wager that one of the switches on this board is not functions. Or the ribbon going to this board or to the spindle motor is damaged. If none of these turn out to be malfunctioning, then you can replace the entire laser assembly (or drive if you don't mind spending extra).

Yikes! This happens a lot on the Pros. A couple times on 1200s. Never seen it on an 1100. The pad on the bottom left goes straight to that via above it. It should be relatively easy to scrape off a little solder mask to expose copper. The other missing pad looks similar, but with the topical copper ripped off of even the via. That one will be hard to solder there and/or re-route. Will require some wire/lugs, some solder mask, and something to glue down the socket to the board once the new "pads" are built. If you're in the US, I'd be happy to do the repair for you as I already have the tools and supplies, and experience rebuilding these.

The only time it will overheat that quickly is if the APU clamp is loose or upside down. Also, you shouldn't turn it on without the other motherboard sandwich plate present. The RAM chips have thermal pads on them and rely on that plate being present to dissipate heat.

What is meant by "don't have a disc drive?" Is there literally not one inside or does it just not work? And if so, does not work in what way specifically? If a PS4 cannot communicate with the MATCHED Renesas chip, it will prohibit an update. Sometimes the inability to communicate is due to a blown fuse. In either case, replacing the drive on a fat will not help because both the Renesas chip and the fuses are on the daughterboard. This is why I asked about don't have a disc drive: Because if the daughterboard is missing or unmatched, there is no getting past this. If the PS4 is on a lower firmware, there is a homebrew workaround. You might have to put the old hard drive back in. If so, you'll want to boot into safe mode and rebuild database before trying to use it again.

White light no display. Check cables, TV input, etc since this occurred after a moving about. Try booting into safe mode (hold power until it beeps a 2nd time) to see if it will display there. If it's a fat as the picture shows, it's usually a damaged port. If it's a Pro as the title says, unless the port is physically loose, it's likely not the port.

Was the console dropped? Have you tried both USB ports? Most common issue here is that the cable being used is charge only. I've also seen a data cable that did not allow for sync. If possible, try and solve for wrong/bad cable first. Assuming controller and cable are good... While the PS4 is off, hold the power button until you hear it beep a 2nd time (about 7 seconds). This will take you into safe mode. It will ask you to connect the controller via cable. If it works here, but not on the home screen, your wifi module is bad. If it doesn't connect here also, then your southbridge is likely bad. If you do have to get down to board level, you can also check to see if the overvoltage regulators on the USB ports are good. Sometimes it can be that the USB port is bad and not the associated chips (not common).

Are you asking how to repair this? 3 of the pads look intact. The one that got ripped up appears to terminate at a via right on top of it. You can scrape the solder mask off of the top of the via. Then solder some 0.2 mm (size not terribly important) tinned copper wire to the via, travelling across where the pad used to be. Or solder in a copper lug. This will serve as a makeshift pad. At this point, you ought to put solder mask down on top of both ends of the wire/lug to help keep it in place. Though you don't have to. Next I'd use some non-conductive epoxy to glue the port to the board in a position where all the legs/pads line up. Make sure you don't have the socket backwards! Then solder each leg to each pad.