I downloaded and updated the client. It did not put an icon on my desktop and I cant find a folder for it anywhere. Any suggestions?

You don't know where you installed the file? The executable is in there. If you don't know where it is, try running a search for lol.launcher.exe

One of the instances that shows up will be your normal LoL executable, the other will be for the PBE.

Click on start and then in the search programs and files tab. Search for lol.launcher.exe and you should find 2, one of the normal client and one of the PBE. Run them both to see which is which.