"Will SeaTools for DOS do something that the SeaTools for Windows won't do?"
Yeah, it'll let you run the program without having to boot into Windows.
Or even without having a hard drive attached at all other than the one under test.
Speaking of which, is that a GigaByte brand motherboard you're using?
After 6 years it's possible that Seagate's on its way out.
Go read this
then go to the beginning of that thread and read all the way through.
Then come back and we'll talk more.