I've had this happen to me before and my first solution was to uninstall/reinstall with the component checked.
This is a pain to do, BUT there is an EASIER way!

Go into the Programs and Features applet and add the component to the existing SQL-Server (row/icon) installation. Select it, then click on CHANGE (you will need your original SQL-Server install DVD or equivalent to do this).

NOTE: it is important that this was launched from within the Add/Remove programs or Programs and Features control panel item INSTEAD of directly from DVD.

Select ADD features, then on the feature Selection page, check the box for Full Text-Search.
Make sure when asked, that you specify the correct SQL-Server INSTANCE(s).