In those cases I am usually trying different things:
- Delete the virtual directory in IIS and publish again, just to make sure that there is no "conflicts" or other files "hanging around" which prevent a correct deployment to IIS
- Check Application Pool Settings and ensure that it's running in "Classic" mode
For the date picker specifically, you can try the following:
- In the component hit the "delete" button for the Drop Down Image in the "Appearance" tab. The image is optional and not needed. If there is no image, then the OS default drop-down arrow is displayed
- Check the language settings of your browser; the calendar wants to display in the language of your browser top language
Also: Have you tried to create another (new) project with the date picker component? Can this be published successfully to the IIS?