sims3launcher.exe no where in my folder

Spycoo16  You can't drag and drop the game to a new computer; it doesn't work like that.  There are registry entries and other hidden files that need to be created in order for the game to work, and that requires going through the process of installing, not simply copying and pasting.

Your best bet is to borrow the CD drive from your friend and install the game properly.  If it works, you might ask your friend if you can buy the drive for some nominal fee, so you can use it going forward; or buy yourself the same model, since you'll know it works with the game.

By the way, if you moved the Electronic Arts folder in Documents, that contains your saves and other user data, not the game's program files.  I can't tell from your description whether that's what you moved, or your game was installed into a different "Electronic Arts" folder, but moving the user folder would explain why you don't see the executable, since that's not where it would be located in the first place.