You should have the "Lookup in Dictionary" in the Services menu. Try using it somewhere else, select a word and hit Ctrl+Command+D. Depending on the speed of your computer, it should take at most four or five seconds before the dictionary explanation appears.
If nothing happens (be patient, it could take a few seconds), check "/Library/Dictionaries/", that's where the dictionaries should be. You should have two of them, "New Oxford American Dictionary.dict" and "Oxford American Writers Thesaurus.dict". If they are there, and you still don't have a functioning dictionary, run "Activity Monitor".
Look under the tab "All processes". There are two processes to look for. A process called "PopupDictDaemon". That's the process that handles the pop up dictionary panels. The other is "Dictionary DashboardClient". That's the one that should handle dictionary lookups in the widget. If either or both are missing, restart your computer and try again. If they still don't show up, there is a problem with your dictionary files. Replace them with copies from the Tiger dvd or another computer.
If only "Dictionary DashboardClient" is missing, it's a problem with the widget. The dictionary client is built in, in the .wdgt bundle, so replacing the widget should do the trick. Copy it from another computer, or get it from the Tiger dvd.