SUCCESS!!!!
I'm going to shout this out to the world now, there are plenty of people out there with this problem, and not even LogMeIn support know how to deal with this!
SO, what did I do? I went in to TroyJam's link and started reading around and began going through the tutorial that would supposedly "remove" the damn icon from the tray.
I entered the command /Library/Application Support/LogMeIn/bin/LogMeInGUI.app/Contents/Resources in Finder, thinking it would get nowhere, since I had already deleted everything LogMeIn related from the computer!
For my surprise, there was still a folder under /Library/Application Support/LogMeIn.
Well, in this folder, there was a command prompt uninstaller, different from the pretty and user friendly uninstaller they provide.
So I clicked on it, entered my system password on the command line when asked for and... VOILÀ!!! It ran like a chicken from my taskbar!
FINALLY!!!
Thank you all guys for your time and help!!
God bless you and your brains! =D