Recently a 2001 Samsung 20GB HDD failed on me. Stopped booting. Spent two days diagnosing the problem after which I isolated the HDD as faulty.
You mentioned that you don't want to spend much time on this. But if anyone else ever is in a similar situation and wants to check the health of their HDD, the best tool atm would be
SeaTools for DOS. Do a short test, followed by a long test. My HDD passed the short test but failed the long test. This tool can be run on HDDs of any make. But it can 'repair' only Seagates.
For booting SeaTools from a USB, I used
RMPrepUSB. Some learning curve there, but after that a very handy software.
I am not an HDD expert. I learned the above from the internet.