Awesome! It's great to see LogMeIn SO concerned about this widespread problem with Hamachi2 that they haven't even had time to officially comment on this thread. Oh, wait, I forgot: Most of us are probably using free Hamachi2, which absolves LogMeIn of any responsibility in maintaining this app and, you know, making it work reliably.
That's right, LogMeIn. Ignore the problem, that'll make it go away. Rather, that'll make users ditch your lousy support (rather, entire lack thereof) by switching to one of MANY alternative zero-configuration VPN clients available online. Then there won't be any users complaining about the "Failed to connect to the engine" problem! What a great fix!
-A Hamachi2 user who was interested in getting this product for his business, but having seen the "support" offered by this company to it's free users, is more and more interested in alternative solutions.
PS: Although a patch to this problem would be wonderful, I am sympathetic to the difficult and competitive business of software development. A simple comment on this thread by a LogMeIn developer, as well as removal of the "Solved!" (because this problem is not solved - nor even addressed) tagline would make me perfectly happy, as it would be indicative that you actually care about your customers.
Having the same issue more or less frequently on different computers (commercial version), but the work around often does not work since the service status is "starting", which means I am able to right click - start it :(