OK your controller card is faulty... You wont be able to see a drive formatted inside the box because they do some hoodoo with the drive to compensate for sat to USB transfer throughput in Drives over 1.5 terrabytes.
1. see if you can disconnect the controller board out of the case connect t to the drive and retrieve the data,
2 See if you can get the same controller or any usb to sata controller from a case (a usb brace my work)

I have a sata may in the from to my computer because I shoot video on SSD's. I had the same issue with a western digital last week. They have specials on seagate 4TB external drives for $99 at my local office supply store and I take them out and reformat them. I cant read them unless they are formatted directly from the sata bus.

 

Hi. I have backed all the data up. So far the Seagate has been working well. But I want to scrap all Seagate stuff and use the drive with my current Sata-Usb adapter mentioned above (that couldn’t read Seagate drive). I have bought two of them just any case. But the question is now, what if they stop working? How to choose the best SATA-USB adapter? I cannot connect my drives internally because I don’t have a desktop computer. Or I can use Dvd socket from laptop. But will it power up 3.5” drive? I work on PC with Windows 10.

 

You bought 2 of the SATA-USB adapters?
If you have all the data off it SEEMS to ME you should be able to reformat using Windows and then be able to use those adapters, or any other standard adapter. (and of course I want to know the brand and model of the adapters you have, but that's just my curiosity )
The drive will be limited to its own SATA2 speed (3 Gbps) and the adapters to their USB speed (2.0 = 480 Mbps, 3.0 = 5 Gbps, 3.1 = 10 Gbps).
Those are theoretical speeds and drive performance varies, but if I was getting other SATA-USB interfaces and might use it with other drives and/or newer computers, I would go with the newest USB version... USB 3.0 if 3.1 is too expensive.

Spoiler: SATA-USB stuff you could buy

I got a Sabrent USB-DSC9 a while back (still $23 on Amazon) to connect various drives to USB 3.0 (even IDE drives).
https://www.amazon.com/Sabrent-5-25-INCH-Converter-Activity-USB-DSC9/dp/B00DQJME7Y
But I some really cheap, too.
If you want an ENCLOSURE I see an Amazon Basics for $20, but I can't see any venting, and i thought that is important (?):
https://www.amazon.com/AmazonBasics-3-5-inches-SATA-Drive-Enclosure/dp/B01MZC303G

Anyway, you could always make your own box to hold the adapter and drive securely using even a cardboard box, a bit of foam padding and some tape!
[EDIT: Oh, I forgot you mentioned using the DVD socket. I am assuming you just want to use it to format the drive so it will work with the SATA-USB adapters (?)
That should be able to power an HDD.

 

Last edited: Sep 27, 2019

Thank you so much taskforce! respect!

 

I don't get tired of recommending external docks to use any internal HDD/SSD disk as external (SATA/USB). I use an older version of this: