OK, so I don't think that would be it. Was SeaTools are fresh download? Really surprised it didn't see the drives, as I believe I can on mine, and we are on the same controller, and you even have a Seagate drive. May need to use the Windows version.
I see the other looks basically a SMART test. Which will read the SMART data on the hard drive, but SMART won't catch every issue.
If you have another drive, you might want to try installing Windows and a game or two and see what happens.
Like I said, I have read where Microsoft has defined the first part of your error code as a hard drive read/write error, but I don't think that negates the possibility of it being a driver cause as well.
Oh, and if you haven't yet, you might want to try some SATA cable swapping to rule that out as well.