First thing to try, unkyUb, is to go back into your program files and open the Adobe Reader folder. Is there a program icon in there....if so, right click on that and in the dialogue that opens, select "copy to desktop...create shortcut".
That should put the icon on the desktop and a double click on that should open the prog.
Does that work ?
If not, you could download a new installer from filehippo, but uninstall the existing prog. before installing the new.