...connection using Secondary Log. I recently looked into my security event file and noticed many Logon/Logoff events that were different from mine (the ones clearly marked with my User Name). The entry is from an Anonymous user running the Remote Access Connection manager and the Secondary Logon service.. what does this mean?

this is due to log me in. some body comes to know of your id and through (log me in) they would have entered your computer.

You can not completely shut down LogMeIn on the controllee machine,

You can disable it, but this still leaves the LogMeIn icon in the system tray/notification area. It also leaves program LogMeInSystray.exe running. Even killing this program with Task Manager does not get rid of the system tray icon. One good thing though, disabling it does disable the two LogMeIn services.
right click on Logmein's icon in the taskbar, and select Disable Logmein - then a minute later enable Logmein