The solution (assuming you have already uninstalled lync, or never had it) is to go through the registry and delete the two or three references to Lync_CoreFiles:
- Click START > RUN, type regedit.exe and press the ENTER key
- Click on HKEY_CURRENT_USER (as HKCR contains no references)
- Click EDIT > SEARCH and type in Lync_CoreFiles then press the ENTER key
- Delete any keys relating to Lync
- Try the install again. You do NOT have to reboot
Note that the install log can be found %userprofile%\tracing\OCBoot.log and it is quite small and reads like plain english.
This appears to be an issue with Office 2013 installs. I have Office 2013 installed without Lync on Windows 8 AND Office 2013 installed WITH Lync 2013 on Windows 7. Even after an uninstall of Lync this error occured. I needed to clean the registry of the LYNC_COREFILES entries.
To give credit, where credit is due, I found http://community.office365.com/en-us/forums/166/p/65551/252428.aspx#252428 to be handy.