Test machine:
Pentium 4M 1.7Ghz
Win XP Pro w/ SP2
512Mb RAM
30Gb HD
.Net Framework 1.0 and 1.1
Windows Scripting Host 5.6

After double clicking the installation file.  It proceeds to 
act like any other Windows Installer.  After accepting 
c:\Python24 as the install directory, I am presented with 
this screen saying that there was an error and that the 
installation has ended prematurely.

FYI, I tried to install over Python 2.3 (as in upgrade) but 
I got the same error.  So I proceeded to uninstall Python 
2.3 and other installed libraries.  I then restarted the PC 
and tried to install Python 2.4 again.  This bug is the 
symptom of this second try.

Please find the screenshot attached showing the final 
screen.

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Can you please run

msiexec /i python-2.4.msi /l*v python.log

and attach the resulting python.log (do NOT paste it into
the SF comment box).

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Please find the msi log file attached.  

I managed to pinpoint the area where it breaks..  It's failing 
on CheckDir with an error 2896.

-----
MSI (c) (88:54) [09:50:38:430]: Doing action: CheckDir
Action start 09:50:38: CheckDir.
MSI (c) (88:3C) [09:50:38:440]: Cloaking enabled.
MSI (c) (88:3C) [09:50:38:440]: Attempting to enable all 
disabled priveleges before calling Install on Server
MSI (c) (88:3C) [09:50:38:440]: Connected to service for CA 
interface.
MSI (c) (88:88) [09:50:38:580]: Entering 
MsiProvideComponentFromDescriptor. Descriptor: 2eAq^]D2g
(8V7Xaq(hoRIngresDBMS>M5KDYSUnf(HA*L[xeX)y, PathBuf: 
1C4F348, pcchPathBuf: 1C4F344, pcchArgsOffset: 1C4F2A4
MSI (c) (88:88) [09:50:38:580]: 
MsiProvideComponentFromDescriptor called for component 
{997FA962-E067-11D1-9396-00A0C90F27F9}: returning 
harcoded oleaut32.dll value
MSI (c) (88:88) [09:50:38:580]: 
MsiProvideComponentFromDescriptor is returning: 0
Action ended 09:50:38: CheckDir. Return value 3.
MSI (c) (88:54) [09:50:38:921]: Note: 1: 2262 2: Error 3: -
2147287038 
DEBUG: Error 2896:  Executing action CheckDir failed.
The installer has encountered an unexpected error installing 
this package. This may indicate a problem with this package. 
The error code is 2896. The arguments are: CheckDir, , 
Action ended 09:50:38: SelectDirectoryDlg. Return value 3.
MSI (c) (88:94) [09:50:38:931]: Doing action: FatalError
Action start 09:50:38: FatalError.
Action 09:50:38: FatalError. Dialog created
Action ended 09:50:39: FatalError. Return value 2.
Action ended 09:50:40: INSTALL. Return value 3.
MSI (c) (88:94) [09:50:40:012]: Destroying RemoteAPI 
object.
MSI (c) (88:3C) [09:50:40:012]: Custom Action Manager 
thread ending.

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Can you please try the following things?

1. Run the script

========== SNIP ============
Function CheckDir()
      Set FSO = CreateObject("Scripting.FileSystemObject")
      if FSO.FolderExists("c:\python24") then
        wscript.echo "1"
      else
        wscript.echo "0"
      end if
End Function

CheckDir()
============= SNIP ==============

in wscript.exe (i.e. save it into c:\x.vbs, then run c:\x.vbs)

2. Report the version of

C:\WINDOWS\SYSTEM32\wscript.exe

(5.6 is too imprecise - could it be that you have 5.6.0.8820?)

3. Install VBScript, from

http://www.microsoft.com/downloads/details.aspx?FamilyId=C717D943
-7E4B-4622-86EB-95A22B832CAA&displaylang=en

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BUG FIXED -- solution below.

1)
BTW I actually thought the installer was looking for 
c:\python24. So I created the folder before running the 
installer again.  But it didnt work.

When I ran the script.  It returned this error:  I used cscript.

c:\x.vbs(2, 7) (null): The specified module could not be found.

2) The version of wscript and cscript is 5.6.0.8825
3) This is latest version because I read that installing the 
latest version of scripting host fixes installation problems.

****

I managed to fix it.  I registered scrrun.dll by typing:
regsvr32 c:\windows\system32\scrrun.dll

Thanks for all the help..

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This is fixed for 2.4.1, which will not require VB anymore.

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Having previously sucessfully installer Python 2.4. I run into 
this same error with both 2.4 and 2.4.1.msi on a new 
computer. Running x.vbs gives me 0. Doing 

regsvr32 c:\windows\system32\scrrun.dll

does not help. cscript shows version info below:

Microsoft (R) Windows Script Host Version 5.6
Copyright (C) Microsoft Corporation 1996-2001. All rights 
reserved.

I have captured a log file but perhaps I'm not the orginator of 
this bug I don't seems to have the capability to upload it.

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This can't be the same bug (maybe the same symptom), so
please submit a new bug report.