Bizarre problem. It sounds like it could be a number of issues (hdd driver, hdd controller, filesystem, BIOS...). Jumper settings?
Is there any utility I can use that doesn't require booting into Windows which will copy all of the files over to the fully functional SATA drive? I'm at the end of my rope here.
If you're intending to use DOS,
Should be fairly straightforward. Simply connect both drives, boot into a DOS environment and begin TestDisk. From there, you should be able to transfer all your files over from your old drive (LFN intact).
Alternatively, try a linux environment such as Parted Magic (joy).