Use Revo Unistaller to do uninstalls. It deletes all those entries that the app's uninstaller leaves on the machine. In other words, why go through all these steps when there is an app to do it for you.
Restart your PC.
Right Click the LogMeIn Hamachi Icon on your desktop, then select "Run as Administrator"
Thank you SOOOOOOOO MUCH! This worked PERFECTLY! :)