I contacted LogMeIn support about this problem and was sent this reply:
"Thank you for contacting LogMeIn.
If LogMeIn Hamachi is listed as an application installed to windows still, try using the MicroSoft fix it tool here to uninstall it:
https://support.microsoft.com/en-us/mats/program_install_and_uninstall
If Hamachi is NOT listed as an installed program, try the following:
If you go to:
- Registry > HKLEYLM > SOFTWARE > CLASSES > INSTALLER > Products
There will be a bunch of folders with a random string of characters at the folder name. When you click on each of these, on the right you will see some information about what is inside this key including the Product Name. If you click on each of these as you go down the list one by one you will find one that either has Logmein Hamachi as the name or there will no program name at all.
This folder/key is what is causing the issue. First, right click the key (on the left side) and select to export and save it to your desktop as a backup, then delete it.
Once deleted, make sure there are no others with no name or Logmein Hamachi in it then try to reinstall.