According to the symptoms outlined below, is the I am experiencing
problem is located on the hard disk drive’s platters or the hard disk
If the system is slow to read the sectors and the data they contain, the hard drive is failing. The problem is the the magnetic media on the hard drive’s platters is degrading to the point of failure. Thus the hard drive is struggling to read the data off of the magnetic media on the platters, thus the drive is clearly on it’s last legs.
In a case like this it would seem like your hard disk drive is simply dying. This is typically related to the physical mechanism of the drive—the platters, spindle and drive heads—failing in some way.
As for what to do, honestly no clear answer. Since you do mention the hard disk drive’s platters, I will say this: If the data on that drive is important to you, opening up the physical mechanism itself to attempt to “fix the platters” will only guarantee one thing: 100% no hope of data recovery whatsoever. Do not ever attempt to open a hard drive mechanism if you care about recovering the data contained on it.
My best recommendation to you is to see if you can mount it again. I assume you are using an external enclosure that is perhaps a USB enclosure? One idea might be that if this is a 2.5" drive mechanism, it’s somehow not getting enough power from the USB connector. And if you have it in an external enclosure, it’s probably being powered by the USB port itself. So maybe getting an external USB enclosure that you can hook up an AC adapter to would help?
But all in all, the behavior you describe is in line with complete drive failure. If there is a desire to recover that data, you might want to investigate sending it to a data recovery service. Which is not a cheap proposition—could cost several hundred U.S. dollars—but of the data is important to you and the drive cannot be accessed by you, a data recovery service might be the best and only hope you have to recover data from that device.