You can file for a patent without a working prototype.  However, your description must be very detailed, particularly the part about what you consider to be novel about your invention.  In legal jargon it must describe the invention with "specific particularity," and allow a "person skilled in the art (meaning field of the invention) understand, make and use the invention."

Also, having a detailed description will reduce your legal costs if you hire a patent attorney to help you prepare and file patent application.

A simple patent application can be done at fixed cost of about $3.5-6K, depending on the length and technology. 
-Daniel Basov
Solton Rosen & Balakhovsky LLP
110 Wall Street, 11th floor
New York, NY 10005
212-344-1744
www.srblaw.net