Le's make this simpleThe SSD is not the problem.
But to make things easy, do the install without the SSD. change that later..
Check the BIOS and see when it was created.
You said 'old HDD'. Sso the Segregate Barracuda 1TB is a new drive?
Install Windows 10 again and create a small partition. About 24 Gigabyte is enough to install windows. Later you can use more of the drive later. But for now, a small partition is easy and quick and side steps a possible hard drive issue.
And it should take hours to install Windows 10.
Tip: If the computer seems to be stuck, try the cap lock o r Num lock keys. If you get them to change, the system is working. But it the keyboard lights stop responding, the thing is stuck.
EDIT: Please explain:
It's an old PC with a few cheap upgrades:
Mobo: Packard Bell ixtreme m5140
How old? Did it come with Windows 10?
What kind and size of HDD did it once have?