From your description it sounds similar to mine except for the float moving with the rod seized. Look in the lower right hand corner of this picture:
http://i47.photobucket.com/albums/f167/Tinys1938/BackInTheCar.jpg You see two sending units. The one on the left is a universal I was using. The one on the right is my original without floats. It's not a good picture but it's the only one I have of the sending unit. If it looks like yours let me know & I'll take a better pic. As the float raises and lowers it turns the central shaft which moves the rheostat in the upper housing. If your's is like this one and the float moves but the central shaft doesn't the gear mechanism is broken. It might be fixable. Let me know. FYI, if we can't fix yours I'll let you have the universal I don't need anymore for a WHOLE lot less that the $50 the vendors get for them.
