We just moved into a home with a Hunter ceiling fan, we found a broken light kit in the garage. Husband bought what we believed was a light kit assembly that was made of plastic. The piece is what is under the light fixture/bulbs & just above the glass globe. It is part of the part where the chain goes through the globe. The part broke because it was plastic rather than metal. I called Hunter, was told that fan #20581 was discontinued. Also told that I didn't need a light kit assembly but a switch/housing assembly. I can't find a diagram to confirm it has the part I need. Again the part I need is between the switch/housing assembly & the globe.

If that switch was for the light kit, you may just need a pull switch(it will have 2 wires attached), some light switches have 3 wires to allow 2 bulbs, the other 2 bulbs and 3rd click is all bulbs, if it has 4 wires, it would be the speed switch.

It appears to only have 2 wires going into the piece that is broken. I am attempting to attach photos

These are very common and available everywhere for less than $5.
Home Depot, Hardware stores etc.
If the Light an Fan are on separate wall switches, the switch could be eliminated and connect the 2 wires at the switch. Now it will work from the wall.

https://www.google.com/search?q=Pull+switch&rls=com.microsoft:en-us:IE-Address&ie=UTF-8&oe=UTF-8&sourceid=ie7&rlz=1I7ADRA_enUS355#q=Pull+switch&hl=en&rls=com.microsoft:en-us:IE-Address&rlz=1I7ADRA_enUS355&prmd=imvns&source=univ&tbm=shop&tbo=u&sa=X&ei=iQ20T5CvD4a69QSBxeXpDw&ved=0CM4BEK0E&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=9f984a8daa766a2&biw=1008&bih=603