Thanks for the very clear answers - those help to clarify the situation. I work in electronics within the data storage industry, not in DR, so here are my comments from that viewpoint.
The repeated clicking is bad news, and given that the power source is "known good" (having been used successfully for another similar drive), then that clearly points towards the drive itself.
I'm not blaming you regarding ESD (which is only one possible guess at this stage), and using a wrist strap is a good step

however as I have received more ESD training and also done more research into this area professionally, it's clear that there is much more to
effective ESD control (especially with modern components with their increased ESD-sensitivity compared with those from years ago), which most people are not aware of.
Assuming that nothing unusual happened during the motherboard replacement, which you could link in any way to this situation (to give us other ideas about the possible cause), then I can see a few options depending on the value of the data, time criticality for getting that data etc.:
- Engage a DR company now - some give free or low-cost evaluations (and reputable companies can be recommended by members here), but if your friend has no sensible budget to pay for a recovery, then don't waste their time; or
- Put the drive in a sealed metallised (not pink) ESD bag, with a dessicant bag, and then into a box with lots of packing (in case the box is dropped), and store it while saving money to engage a DR company later; or
- Give up and ditch the drive (be aware that the data is not necessarily beyond recovery, so if there is any personal data on the drive, I would destroy the platters and not just give the drive for recycling "intact"); or
- Take a slim chance on the unlikely possibility of a PCB fault (specifically a damaged Read Channel component) is the cause of your problem, and not heads, preamp, firmware or other internal problems. In that case, a compatible replacement PCB (and transfer of the necessary component(s) from the existing PCB to the replacement) just
might fix the drive - but with these specific symptoms it's a long shot IMHO, and you could easily be spending money for no benefit, and that money could have gone towards paying a DR company for their work.
I'm not an expert with matching PCBs (there is a different section of the forum where people can look for sellers of PCBs), and personally I probably wouldn't bother trying a replacement PCB, but if your friend decides that it's a max $100 budget (for example), then that would likely eliminate any professional help, but a PCB replacement might be possible.
Other people may see further options for you, but you earlier asked for views, so you've now got mine - which is worth exactly what was paid for it

Good luck!