Hi,
Based on the error message, please try the following steps:
1.Press Windows Key + R combination, type put regedit in Run dialog box and hit Enter to open the Registry Editor.
2. In the left pane, navigate here: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\AppCompatFlags
3. At this registry location, as shown in above image, right click over AppCompatFlags key and select Export. Save this key as registration file at a convenient location on your system for backup purpose. Now right click the same key, i.e. AppCompatFlags
and select Delete.
4.You can now close the Registry Editor and reboot the machine. After restarting the system, you can re-try to install Office 2013, in Clean Boot State.
More reference:
http://answers.microsoft.com/en-us/office/forum/office_2013_release-excel/cannot-install-office-2013-error-microsoft-office/e73faec4-3d6c-4a95-b610-4510a6011a55?page=1&tm=1428061032921
Regards,
George Zhao
TechNet Community Support