First thing that comes to mind it that the little lever (actuator) on the brakes is adjusted to far back on the splines. Wire wheel the shaft end (outside) and the actuator arm. There are little dots (dimples) for alignment. If it is aligned to far back you will not get the rotation you need for good solid brakes.
Brakes should be pretty simple for you to troubleshoot. Here is what I would suggest.
1 - remove rear tire from brake side / remove brake drum cover
2 - remove brake drum
3 - work foot brake pedal - can you see it actuating the little cam and making the brake shoes expand?
if no check brake linkage and be sure cable is set up correctly and not broken or stretched
4 - replace brake cable if needed
5 - does the shoes actuate out now?
if yes, measure the widest part (shoe to shoe) when brake pedal is fully engaged
now measure the inside diameter of the brake drum. The shoe measurment should be bigger. If it is not, replace brake drum. An ad placed in the classifieds here on the boards would have a 110 brake drum out in the mail to you shortly.
replace worn drum with new one.
once drum is installed - turn the axle and operate the foot brake pedal. Do you have brakes now?
If not, we'll need some photos as something may be wrong - bad parts or something,
Hope that helps.
BTW - maybe pics of the current setup will save some time too. Post a pic of the linkage between the pedal and the cable, and also a pic of the rear brake actuator - (little part that cable hooks to on the brakes).
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