Sorry, I seem to have lost contact with this thread for a few days - no idea why !
Your #27 :- CD / DVD drive = optical drive . The two terms are interchangeable and mean exactly the same thing, a drive that will read and write to a CD or DVD.
Your #32 and #33. Taking a hard drive from one computer and plugging it into a spare SATA connector on another (you need to connect power to it as well) is a very common servicing technique but you DO NOT disconnect the hard drives in the computer you are temporarily plugging it into. If there is a shortage of SATA connectors you can disconnect one drive, but definitely NOT the one with that computer's operating system on.
The reason is that your hard drive contains system specific files for running your computer, and the hard drive in the other computer contains specific files for running that computer - and needs them to make it run.
You connect your hard drive to another computer to see if your hard drive is working, to see if you can read and write to it, or even just to see if it can be recognised in Windows Explorer.
When you connect your hard drive to the second computer, what I would expect to see in 'Computer' or 'Windows Explorer' is :-
C:\ - the drive with the second computer's OS on it.
D:\ - the second hard drive you say is installed on this computer
E:\ - the CD / DVD drive (optical drive) installed on this computer (some systems only list CD/DVD drives when there is a disc in them)
F:\ - YOUR hard drive from your computer.
If your hard drive doesn't show up here, try a re-boot with it still connected. Then see if it shows up this time. If it doesn't, the drive is probably dead. Assuming it does show up, then you will be in the happy position of being able to copy all the important data - your own stuff - to an external drive, and then be able to run the Seagate diagnostic on your drive.
Back up your data - ie copy it to another drive - BEFORE you run the Seagate diagnostic. If the Seagate diagnostic shows a lot of problems with your hard drive, well you have your data backed up and replacement drives are reasonably cheap.