It looks almost as if you have two instances of calibre installed or the installation of 3.27.1 is being blocked.
When you look in Apps and Features, does it show only one instance of calibre installed? You can also try opening a command prompt and typing "where calibredb.exe" without the quotes and hit enter. This should return "C:\Program Files\Calibre2\calibredb.exe" for the normal install. This does assume that the path to the calibre executables is in the system path variable.
Code:
C:\Users\David>where calibredb.exe
C:\Program Files\Calibre2\calibredb.exe
C:\Users\David>where calibre.exe
C:\Program Files\Calibre2\calibre.exe
C:\Users\David>where where.exe
C:\Windows\System32\where.exe
If only one instance of calibre shows as installed, you may want to uninstall calibre which should not affect your library/plugins/etc. and then re-installing.