How do I build the support structure for a 36"x14' built-in desk?
This may be ridged enough,  however I would recommend going with a torsion box design.  This is how a professional furniture maker would attempt this.  You can use 2x4 for the "core" and two skins of 3/4 inch ply.  I would put a perimeter of 2x4 around the core (not shown in the picture) then lag bold the perimeter into your studs.  You may have to cut a hole in the bottom skin to make this work.  The key to making this work is to glue (subfloor adhesive) and screw (2") the skins to the core.    Woodworkers have been using torsion boxes for years to create large desktops. 

If you are using standard 8' plywood for the skins you will probably want to stagger the seams between the bottom and the top tortion box.  For instance in the top use 2 7' pieces of ply.  In the bottom skin use a 3' a 8' and a 3' piece of ply.

This will probably be your safest best.  After you build it and before you install it you can test it out with two saw horses.  I would be very surprised if it did not hold 200 lbs or more.   

if you are still worried about flexing move up from a 2x4 to a 2x6 for the core and you should be able to support several people standing on it.