Thanks for the update.
JorFor wrote:I think I already checked whether the "Samsung drive spins-up immediately & stays spinning, when attached via the PC's SATA & power"; I think it started spinning, but then it stopped after a few seconds. I'm not sure right now, cause I did it a couple of weeks ago. I will try it again in the weekend.
OK, I'll be interested in the result. The reason for the question is related to the PC's power supply to the drive. One possible reason for the drive working when attached via USB & therefore using an external PSU, is that the PC's internal +12V supply to the drive could be out-of-spec, and only drives (and some fans) use +12V in a typical PC, so the PC may appear to work OK, even with +12V out-of-spec.
Do you have any other SATA drives (spare or in-use)? If so, and if you are prepared to take a risk, you could move one to use the same power & SATA connections as the Samsung drive, and see if that drive is recognised by the BIOS (although this isn't a
conclusive test).
[Edited to add: If the Samsung drive does indeed stop spinning when using the PC's internal power, as you think you remember, but works OK using external power from the USB adapter, that is a potential indication of a problem with the PC's power supply to the drive.]
JorFor wrote:2) I assume that if the contents can be accessed via a USB connection, then the HDD is OK. Am I wrong to assume this?
Wrong assumption IMHO

The drive
may be OK, yes, but I can think of a couple of drive failure mechanisms, that would cause the drive to work via USB, yet not be recognised by the BIOS. Therefore personally I'm not assuming that the drive is OK.
JorFor wrote:3) As I said, my PC has an OEM version of Windows XP with Media Center, and I understand I'll lose it if I change the HDD.
I stopped doing Windows sys admin some years ago. You'll need to find a Windows support forum if you want to ask someone about that. For what it's worth (which isn't much!) my recollection is that even the OEM WinXP versions did allow an HDD to be changed, without needing to be re-authenticated, if that is the only component which changed - but I could be wrong.
If you have a spare disk, at least as big as the Samsung, you could test this by cloning the Samsung onto that spare disk temporarily (don't boot Windows with them both installed at the same time!), and see if Windows complains when booted from the other disk.