hmm, not sure you need a widget to get a drop down menu, this should be a CSS controlled item.
do you have a link?
Also do you have your Appearance > Menus set up correctly? You need to have your sub menu items (drop down menu items) indented underneath the main menu item:
Main Menu Item #1
Sub Menu Item #1
Sub Menu Item #2
Main Menu Item #2
Sub Menu Item #3
Hopefully that gives you the idea. You need to drag the sub menu item underneath the main menu item you want it to show under. It should indent if you play with it a little.
Also does your theme support the menus?
Here's a general page about the menus:
Here's a page about adding support to your theme:
This page talks about adding the placement of the menu to the theme:
Even if you get all that in the right place, you'll still need your CSS to handle the drop down menus.
If you have a link that is really helpful. If not, you might use pastebin.com to copy your entire HTML page code and link to it here so people can trouble shoot it. (Please don't paste your entire page code here, use pastebin).