As above its dead, its a Maxtor drive which arent well known for being reliable.
You can open it if you want but if its not dead....that will probably kill it as opening a hard drive in a non clean room is never a good idea.
https://www.dummies.com/computers/operating-systems/windows-10/how-to-change-the-location-of-user-folders-in-windows-10/
Nice simple guide on how to do this
If you have the money sure stretch out for an SSD you cant go wrong but for the cost a hard drive will do what you need just fine as long as its 7200 rpm
Basically just restart the PC it restarts all the Windows services, you'd be surprised how many times thats fixed similar issues for users where i work
Im guessing you have tried another known working power supply?
I have seen in the past that just because a power supply turns on with the paper clip method doesnt mean it works correctly when it has any sort of load on it,
its a 50/50 as it could still be a motherboard issue (which it sounds more likely)
Are these mechanical hard drive's or SSD drives?
What is the transfer speed showing as when disk usage is 100%?
Are there any disk errors in event viewer?
The fact you can format the drive without an issue tells me that its not a drive issue but more something strange within Windows.
I'm going to sound like an absolute standard IT technician when i say this but im guessing this machine has been restarted to restart all the services?
Yea its a good drive for the price but like any hard drive, no matter how good people say it is, it may fail in a week, or a few years, just keep a backup!
If you dont mind erasing the drive do the following:
Open CMD as administrator
Type the following commands, press enter after each line
Diskpart
List disk
you should now see the drive capacities, (hopefully here it shows as 2TB)
now to select that disk type : Select disk X (x being the drive number that shows on screen)
Type : clean
Once cleaned go into disk management and initialise the disk ( i normally do it as GPT)
Then you should be able to right click on it an format is as a new volume.
I hope this helps!