They have the Office 2003 icon for the respective files (Word or Excel).
To be specific about the process, I first copied the "once deleted" files to the PC where the original disk was put as slave for recovery.
There was no way to open the files from the hard Disk in which I first copied them. In fact, trying to open the files from the GetDataBack browser itself (in effect, that is like trying to open the files from the original disk, the one that was beign recovered) gave the same error. That is why I personally (but, maybe I am mistaken) have discarded the possibility of it beign a problem related to user rights and whatnot.
Thanks for the fast reply.