Recover data from one failed HD in MyStudio II 1 TB

My MacPro running Snow Leopard has stopped recognising the My Studio II 1TB. On running disk utility, sometimes the disk is shows up, sometimes not. But even when it shows up repair function does not work.

I removed the two 500GB drives from the enclosure and attached directly to the drive bays in MacPro. Only one of the drives is recognised by Disc Utility, but even the one recognised by disc utility  does not show up in Finder.

I connected the drive by USB on my MAcBook and it shows up with disk utility but not on finder.

How best can I retrieve files from the disks, before requesting for a replacement?

Depends, if you had a RAID 0 (It’s non-recoverable by design) then you can’t recover the data. If you had a RAID 1 then you’ll just need a recovery software like disk warrior to scan the drive at a low level if it’s seen on disk utility.