Try repairing Apple Software Update before trying to remove it.
For general advice see Troubleshooting issues with iTunes for Windows updates.
The steps in the second box are a guide to removing everything related to iTunes and then rebuilding it which is often a good starting point unless the symptoms indicate a more specific approach.
Review the other boxes and the list of support documents further down the page in case one of them applies.
The further information area has direct links to the current and recent builds in case you have problems downloading, need to revert to anolder version or want to try the iTunes for Windows (64-bit - for older video cards) release as a workaround for installation or performance issues, or compatibility with QuickTime or third party software.
Your library and device backups should be unaffected by these steps but there are links to backup and recovery advice should it be needed.
If the issue persists and you have a 64-bit system try the for older video cards version which is a 64-bit installer for mostly 32-bit code, similar to all 64-bit versions of iTunes up to 12.1.
If you've tried the above without success then see the method in Install missing components. What component fails to install, and what error message does it give? See this post for steps to produce detailed logs of the installation which may reveal why iTunes won't install. Look for words like failed or error.
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