Hi Ken,
You have pictured a Free Vibrating shuttle sewing machine. A more specific model can be found in Needlebar website:
http://needlebar.org/cm/thumbnails.php?album=298&page=1
Good chance the cabinet goes to the head. I have a similar Free machine that uses 15x1 needles and a pretty unique shuttle that would be difficult to replace. Sort of looks like the spring on top of the arm is broken which might present a problem replacing.
Probably not an ideal first treadle sewing machine for use. How's the Singer next to it look?
Jon