Can you please provide the two log files in the C:\Users\YourUserID\Local\Temp\Adobe_ADMLogs directory (since this is a Windows XP machine, the user's directory is in the 'Documents and Settings' directory.) These will help us troubleshoot why the error is occurring. Upload the files to cloud.acrobat.com/send using the instructions at How to share a document.
The offline installer is available at the bottom of the Installation problems | Flash Player | Windows page in the 'Still having problems' section. You can use the same for and share the link of the files uploaded here.
Thanks for posting the files. We will look into the same.