ok, i've fixed i but i'm not sure what the key process was!
i tried uninstalling and reinstalling as noted - didn't help.
i then uninstalled and reinstalled and chose to discard the user settings - didn't help as i was unable to log back into the hamachi login service.
i uninstalled again and followed the steps here: https://community.logmein.com/t5/LogMeIn-Hamachi-Discussions/Cannot-connect-to-logmein-login-service-try-again-later/td-p/127812 - scroll down to the excellent post by PiscisKnight. Basically it says "do the install using IE not Edge, Chrome or Firefox"
and it now works!
whether it was the discarding of the uesr settings or the use of IE, i don't know but it's worth a shot if nothing else has worked so far for you!
K