Audacity downloads are here: Audacity ® | Download for Windows. If you download elsewhere you may get viruses or versions of Audacity not made by us.
Please be careful with XP. It is a security risk given Microsoft no longer supports XP with patches. See audacity not saving - #3 by Gale_Andrews
If you have a download manager, turn it off or you will get the same corrupted download each time. Clear the download list in your web browser for the same reason.
If this was 64-bit XP, the only valid reason you would get that error with a correct download and properly functioning system is if you downloaded a 16-bit application. For 32-bit XP you would get that error with a 64-bit application. Audacity is 32-bit so that does not apply.
When you have redownloaded from us, you could try right-click over the installed/unpacked audacity.exe > Properties, then try different compatibility settings.
Even if that works, run a complete overnight anti-virus check. You need to do that at least once a week on XP.
See Windows 7 and .exe is not a valid win 32 application message - Microsoft Community for some file system checks you can make. Or just backup your data and reinstall Windows, or (safer) install a version of Linux.
Gale