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test_1686475 of test_os appears to rely on the
existence of "pagefile.sys" on the C drive like so:
def test_1686475(self):
 # Verify that an open file can be stat'ed
 try:
 os.stat(r"c:\pagefile.sys")
 except WindowsError, e:
 if e == 2: # file does not exist; cannot run test
 return
 self.fail("Could not stat pagefile.sys")
But since pagefile.sys may not be on every C
drive and since the exception object e is not a numeric then that test is probably going to fail if the pagefile.sys does not exist where it is expected.
In such a case Windows returns "[Error 5] Access is denied: 'c:\\pagefile.sys'". So we need to test if e.winerror == 5 to skip this and return without failing.
Patch "test_os.patch" is attached. 
By the way, I see the same problem in the trunk, so maybe this need to be applied there as well.

Please see http://www.python.org/sf/1686475 for reference.
Martin,
I think you should be checking for ERROR_ACCESS_DENIED not ERROR_SHARING_VIOLATION as you do in your patch to r54685 and r54686. The attached posixmodule patch fixes this issue for me on MinGW. Can you try it out?
File Added: test_1686475.patch

Why should I not check for ERROR_SHARING_VIOLATION? The OP complains that he sees an error "The process cannot access the file because it is being used by another process" in 2.5.0, and can stat the file in 2.4. So it is clearly ERROR_SHARING_VIOLATION that is being returned (also on the system on which I developed the patch).

I had thought that the file was opened exclusively by Windows
and so the latter denied access to it (including sharing). 
However, it might be worth a while to note how others handle 
this problem. 
Please see ntfs.c of MIT/GNU Scheme:
http://www.koders.com/c/fid3A61BD3B46FA62F5E9F99E5860DCAE5BC2B7FA2C.aspx
and ntfs.h of the same project:
http://www.koders.com/c/fid5FA9A6766ABABAAB4DC09266CA61866F8270A139.aspx
They actually test for both errors in addtion to ERROR_DRIVE_LOCKED to determine if stat has worked or not.
Regards,
Khalid
More references:
http://www.supportnet.de/stat/2002/7/id98848.asp
http://www.cygwin.com/ml/cygwin/2000-01/msg00274.html
http://ftp.gnu.org/gnu/mit-scheme/stable.pkg/7.7.1/changelog.txt

Another source seems to suggest that the error message will
differ depending on the Windows version. I think the error 
message might be more related to the underlying file system. 
Hence since my C drive is formated as FAT WinXP might be 
reporting attempted access to the locked pagefile.sys as ERROR_ACCESS_DENIED, however, in other machines where the 
C drive could be formated as an NTFS then the error message 
will be changed to SHARING_ERROR_VIOLATION. 
This makes sense because pagefile.sys seems to be opened 
exclusively by Windows in either case. The error differs 
depending on the capability of the file system. And so one 
would be expected to test for both errors to see if stat 
worked.
Regards,
Khalid
Reference [Search of ERROR_SHARING_VIOLATION] in syscalls.cc of Cygwin:
http://www.koders.com/cpp/fid05B16888E9827D2766C45C718ED8620BC82B4DCE.aspx
pagefile.sys

The Modules/posixmodule.c patch needs tests.

@Brian/Tim the attached patches have not been applied, what do you make of this one?

Now the test (see Lib/test/test_os.py:470) has been changed to:
try:
 os.stat(r"c:\pagefile.sys")
except FileNotFoundError:
 pass # file does not exist; cannot run test
except OSError as e:
 self.fail("Could not stat pagefile.sys")
so this should work properly now.
I can't find the code changed by the second patch in Modules/posixmodule.c, so I'm going to close this issue as out of date.