So you got compiz reinstalled?
Then, since you don't have icons, I guess, install the compizconfig-settings-manager through a terminal
, and when installed open with ccsm in terminal and look for the unity shell plugin and make sure it is checked(enabled).
sudo apt-get install compizconfig-settings-manager
You'll need to actually click on the unity shell plugin icon-thingy as unlike others the enable function is in it and not like the others that can be checked without entering the various categories.