This seems to be quite a common issue in Office 2013, you install Office 2013 and it appears to install correctly. Then when you go to launch Word 2013, Excel 2013 or any other Office 2013 application then you find there are no Icons on the start menu or desktop for Office 2013. When you go to control panel however Office 2013 looks like it has installed correctly.
This is a known issue with Office 2013, to fix we need to uninstall Office 2013 and remove some keys from the registry. To uninstall office 2013 go to control panel then programs and features. Then locate Office 2013 and select uninstall as seen in the image below.
Once removed run regedit ( Windows key + R then enter regedit ) then make sure the keys below have been removed, if not remove them.
32-bit versions of Microsoft Windows
HKEY_CURRENT_USER>Software>Microsoft>Office>15.0 HKEY_LOCAL_MACHINE>SOFTWARE>Microsoft>Office>15.0 HKEY_LOCAL_MACHINE>SOFTWARE>Microsoft>Office>Delivery>SourceEngine>Downloads>*0FF1CE}-* HKEY_LOCAL_MACHINE>SOFTWARE>Microsoft>Windows>CurrentVersion>Uninstall>*0FF1CE* HKEY_LOCAL_MACHINE>SOFTWARE>Microsoft>Windows>CurrentVersion>Installer>Upgrade Codes>*F01FEC HKEY_LOCAL_MACHINE>SOFTWARE>Microsoft>Windows>CurrentVersion>Installer>UserData>S-1-5-18>Products>*F01FEC HKEY_LOCAL_MACHINE>SYSTEM>CurrentControlSet>Services>ose HKEY_CLASSES_ROOT>Installer>Features>*F01FEC HKEY_CLASSES_ROOT>Installer>Products>*F01FEC HKEY_CLASSES_ROOT>Installer>UpgradeCodes>*F01FEC HKEY_CLASSES_ROOT>Installer>Win32Assemblies>*Office15*
64-bit versions of Microsoft Windows
HKEY_CURRENT_USER>Software>Microsoft>Office>15.0 HKEY_LOCAL_MACHINE>SOFTWARE>Wow6432Node>Microsoft>Office>15.0 HKEY_LOCAL_MACHINE>SOFTWARE>Wow6432Node>Microsoft>Office>Delivery>SourceEngine>Downloads>*0FF1CE}-* HKEY_LOCAL_MACHINE>SOFTWARE>Wow6432Node>Microsoft>Windows>CurrentVersion>Uninstall>*0FF1CE* HKEY_LOCAL_MACHINE>SYSTEM>CurrentControlSet>Services>ose HKEY_CLASSES_ROOT>Installer>Features>*F01FEC HKEY_CLASSES_ROOT>Installer>Products>*F01FEC HKEY_CLASSES_ROOT>Installer>UpgradeCodes>*F01FEC HKEY_CLASSES_ROOT>Installer>Win32Asemblies>*Office15*
Once done reboot your pc and install office 2013 again.
Check out Microsoft guide on manually removing Office 2013.