I always have to 'press' manually the power button to go online after a restart. I use the Hamachi network to provide remote support and cannot do easily so if someone has to login to the box and 'press' the power button to go online. I found no solution in the forums and help.
I use today the Windows client version 220.127.116.119 and am on Win10 64bit
On a 2nd PC, as a virtual PC, same OS, Win10 64bit, I have the same Hamachi client, with the same version, build number .579 I have no trouble whatsoever and Hamachi starts fine automatically (e.g. logs in and goes online) after every reboot.