Have you trying to install SharePoint 2013 in a machine where you had SharePoint 2010 previously installed and removed?
If that is the case, you may get this error message ” Setup had detected previous versions of this product on your computer” while you install even though you removed SharePoint 2010 completely from your server.
Uninstalling SharePoint 2010 does not remove everything and there are still some items exist in the server like /14 folder , SharePoint Web Services Web application and its application pool in IIS but you also need to remove settings in regedit. If you don’t this is what you will get
Setup had detected previous versions of this product on your computer. Setup can’t continue while these are installed. Please remove the previous version before restarting this version’s setup program. If you want to upgrade your existing content and services, you should review the upgrade documentation to determine the correct process to use for your environment.
1. HKLM\Software\Microsoft\Shared Tools\Web Server Extensions\14.0
2. Delete all the folders under 14.0
3. Try the installation again