I have had that problem with the dual application launcher menu before on Linux Mint KDE 13 but it's been a while, I did not lose the system tray however.
I am pretty sure the application launcher was an easy fix, but if you see in the future, the first thing to do would be to delete the panel and start a new one, and here is where you would add a system tray as well. I followed the same course as you for a while, but you are going to have to stop and deal with what is going on within the OS instead of constantly replacing eventually. I'm sure it could be said that KDE is not for newbies..blahh. Thing is, the more you fail, you will most likely be learning, for me this is preferable. As for the DE you switched to, that is 3.4 most likely, some of those environments do not work as par for course..like Gnome, never seen it work, but I have a Gnome session entry on several OS that does nothing, it is like a leach. This is why I recommended 3.4 lite. It looks great, has all the options, and you can just deal with Mate and move from there. I like Mate, it just doesn't look like this
That's just moving files on a barely set up sid, and it is beautiful.