Manually delete the Hamachi2Svc service as the local administrator.
I was experiencing the same problem trying to reinstall a Hamachi installation that had become corrupted during a Windows 7 -> Windows 10 upgrade. Changing privileges on the C:\Users\%USERNAME%\AppData\Local\Temp directory had no effect. The installer kept telling me it had found a previous version of Hamachi on the computer, prompting me to update, but the installer failied with the DLL error everytime.
I performed a manual uninstall of the program, stopping the service, uninstalling Hamachi from the Device Manager, deleting the Hamachi.sys driver, all the Hamachi directories and all the main Hamachi registry entries but the installer was still failing with the same message. Only after I manually deleted the Hamachi2Svc service was the problem resolved, allowing me to install successfully. I believe the default account running the service may have been changed in the past, causing this issue.
Steps as delete the Hamachi service:
Open the Start menu, click the Search/Run box, type cmd then press CTRL + SHIFT + ENTER (this runs the command prompt as the local administrator account).
Type sc stop Hamachi2Svc and hit enter (stops the service).
Type sc delete Hamachi2Svc and hit enter (deletes the service).
Hopefully you will no be able to re-install Hamachi, unless something else is causing the issue.
Any further issues could be caused by restricted access or data corruption to directories and/or registry keys, so you will sometimes need to 'take ownership' of said directories/registry keys in order to delete them, assuming no physical disk corruption.
The Microsoft Uninstall/Install Repair Tool worked for me.
Now, I had a slightly different issue, which I think was prematurely deleted registry entries for Hamachi that were preventing proper installation via the built-in Windows installer. As a a result, I couldn't reinstall Hamachi, because the Windows registry entries apparently indicated that it was still installed.
The MS tool turned up two unnamed programs. Trying to fix the first one did me no good, but when I told it to fix the second one, that did the trick. For some reason, my Office 365 installation became corrupted, but reinstalling that fixed it right up.
So, thanks for the suggestion and I hope this info may help someone else.
the solution was simple but after wasting so much time with the absurd suggestons in this thread, and knowing how miserable logmeinsupport is, i don't want to share it. Let other people learn how horrible logmein service and support is and stop using it. thought they might get better having been bought by citrix but i suspect citrix just bought them to put them out of business and absorb their customers into their gotomypc family. fortunately there are alternatives and they acutally cost less. Was ok with paying more for a company that had support only to learn it is miserable.