I’ve had that issue. The platters were good, the circuitry was blown by a power surge that got through a metal-oxide varistor power-surge protection power strip (they are actually good to stop only one surge, then they act as only a power-strip). The data was extremely valuable for a client, and of course he had not bothered to back it up.
I bought a working hard drive that matched exactly his old one(which took some doing to find), and carefully replaced the circuit board. When I re-inserted it in the computer it booted perfectly. It resurrected all the data and I proceeded to make several backups. I still did not trust it with my rebuild with new electronics for everyday use, so we put in a brand-new, larger HD and re-installed the OS and restored everything from one of the backups. It was expensive to do, but worth it due to the value of the data.
Unfortunately these days you usually have to do an extra step... First you have to find a matching board, then you have to find the eprom on the boards and use a heat gun to pull them off and do a swap. Most boards are programmed not to work if the info on the eprom does not match the info on the hard drive. You can sometimes do this with a cheapo heat gun and covering the rest of the components on the board with aluminum foil, but heat guns made for this purpose can be found for less than a hundred dollars.
I just had this type of failure on a hybrid hard drive. This was out of my league. Most of my data was backed up but I still lost quite a bit of 3-D modeling that I had done designing stuff for me 3-D printer. It is more of a hobby, so I wouldn't say it was truly valuable but there were many hours of work into it. I had been saving my work in a directory picked by the software that I use and didn't think about it not being backed up, until it was gone. Fortunately, I just found a place that will evaluate the board and charges just $60 + $15 for shipping if all your PCB board needs is a diode swap, a reset, or some other simple repair that doesn't need a clean room but is a little beyond the capabilities of most of us. That is a fraction of what normal data recovery costs... so we will see how that goes.
Your trick of dropping the old desktop computers a few inches to reseat the socketed chips reminds me of the laptop motherboard repair that I used to do to a lot of friends computers when they went on the fritz. I would take the heat sinks off the gpu and cpu and cover the rest of the motherboard with aluminum foil and have someone hold the laser pointer from an infrared thermometer on the surface mounted chip that I was heating up with the heat gun. This usually brought these laptops back to life for a while longer, but sometimes it would kill the thing off completely, especially if some little resistors came loose or the chip was what was actually starting to fail. They mount surface mounted components under extremely precise conditions and typically with some type of robot.