If a correctly made (virus free) boot disk/CD can't recognise the primary
hard drive, it cannot format it.
My aged brain cells recall - several months ago in this NG - reference to a
Seagate disk utility (diagnostic and repair, if memory correct) which worked
on other manufacturer's disks too.
I'm open to correction here, but your description is that of a (s)crap HDD.
(hope you had back-ups!)
Whether the HDD is recoverable is debateable. Try the Seagate site (or
Google) for the diagnostic tool and run it - you can't get in any worse
state than you are already!
You mentioned, early on, the presence of malware - could be a virus has
totally corrupted the boot sector.
Another possibility is terminal (mechanical) drive failure
Other solutions - professional disk recovery service (results not
guaranteed, their charges are)
or, just write off that HDD and replace with
another.
Whether or not your SECOND hdd also has malware/virus, you will only
discover when you have a formatted bootable primary hdd and OS. When you get
one, recommend first action is to virus-scan the second HDD, to avoid any
possibility of re-infecting the primary HDD.
Hope this helps, and good luck - Len.
