Let Reader Submit Quick Question

I’ve done what I believe to be an exhaustive search of the plugins but I can’t find anything that will do what I need.

I want to be able to add a small “form” to my sidebar, where a reader can type a short question. The questions can then be saved in the database or emailed.

The concept is to allow submissions for a sort of “Dear Abby” functionality.

Does anyone know how I might be able to accomplish this?