Welcome to OCC!!
A 2165 has a hydrostatic transmission. No friction plates. I'm not sure what site you got that info from, but it is incorrect. I suggest a fluid and filter change. Best place to get cub cadet parts, is from
http://www.cubcadetpartsnmore.com/ You will have to get your part numbers form either the Cub Cadet home page, or partstree.com as the site I linked to doesn't have you model numbers diagram. Just because I'm feeling nice to day, I'll save you some trouble. The filter you need is a 51410 Wix filter available from most auto parts stores. The fluid you need is a hydraulic transmission fluid, which can be purchased through CCC, or at most any place oil is sold. I suggest a tractor hydraulic transmission fluid if your not going to use the Cub Cadet suggested Hy-Tran. (I'm not going any deeper into fluids as that is a touchy subject here.)
I'm also going to suggest you remove the fenders and clean up the machine. Lots of PO's (previous owners) don't take good care of their cubs allowing grass to build up on the hydro. A hydrostatic transmission is air cooled and this dirt buildup makes it run hot. Which will also weaken it. Clean it up good so it runs cool, do a fluid and filter change, and if that doesn't fix it come back and we'll help some more.
Here on OCC, we like pics so if you have a chance post one of your machine!