HERE IS THE SOLUTION... TADAN!!!
Looks like some people are REALLY frustrated at this problem. HERE IS THE SOLUTION, TADAN...!!!
I also migrated to Win 7 x64 from Win XP x64, and still used the same Enterprise Edition 2007, with choosing to save documents as "doc" option instead of "docx". And my father started getting this problem. Now not like this was the first time for this problem. I remember this problem being a PIA (pain in the ass) even many years back; and you can even get old forums on the net (probably all of them unsolved of course!).
I had to research a bit. I created a "doc" by copying the contents of one such document, on the desktop, worked fine. Pasted in E:\My Documents
(where I store all the app docs), could not save. I pasted the same in D- fine again! So is something wrong with the folder E:\My Documents? I pasted just in the E drive, and problem again. Of course now you know the problem, and probably even the solution.
Considering I had not formatted this E drive since my last OS, I guessed that even the permissions from a last OS have to be owned on the new OS before a folder lets you open it. But permissions are a very strict matter. So I thought that may be the old boot information of drive E is messing with the new boot information of the Word application that is running from drive C, the newly formatted drive. And I had formatted even drive D a couple days ago, after Win 7!
And so, I moved all the E data to drive D, formatted E (a full format; though a quick should be all you need), then moved data back again, and the problem is gone.
Now, they don't call me R&D man just like that. I am like that in everything. (Incidentally, don't use the "Move" command; ALWAYS use only the "copy" command which is risk free. I had multiple backup so I used "move", though even then "move" was useless.)